Use synthetic division to find the quotient and the remainder for the problem: (12x^4 + 5^3 + 3x^2 - 5)/(x+1)?,

Answers

Answer 1

Step 1 : Setting up the problem

Write the coefficients of the dividend in the same order. For missing terms, enter the co-efficient as zero. Set the divisor equal to zero and use that number in the division box.

The problem now looks as follows:

-1 | 12 5 3 0 -5

Step 2 : Bring down the first co-efficient and write it in the bottom row.

-1 | 12 5 3 0 -5
______________________ 12

Step 3 : Multiply the first coefficient with the divisor and enter the value below
the next co-efficient. Add the two and write the value in the bottom row.

-1 | 12 5 3 0 -5
_____-12_______________ 12 -7

Step 4 : Repeat Step 3 for rest of the coefficients as well:

-1 | 12 5 3 0 -5
____________7 ___________ 12 -7 10

-1 | 12 5 3 0 -5 ______________ -10______ 12 -7 10 -10
-1 | 12 5 3 0 -5 ____________________ 10_ 12 -7 10 -10 5
The last row now represents the quotient coefficients and the remainder. Co-efficients of Quotient are written one power less than their original power and the remainder is written as a fraction.

Answer :12x^3-7x^2+10x-10+5/(x+1) where the last term denotes the remainder and the rest is the quotient.

Answer 2

Final answer:

To use synthetic division to divide a polynomial by a linear expression, follow the steps: arrange the terms, change the sign of the linear expression, bring down the coefficient, multiply and add, write the result, and determine the quotient and remainder.

Explanation:

To use synthetic division to divide a polynomial by a linear expression, follow these steps:

Arrange the terms of the polynomial in descending order of their degrees.Change the sign of the linear expression you're dividing by.Write down the coefficient of the term with the highest degree of the polynomial and bring it down.Multiply this coefficient by the changed sign of the linear expression and write the result under the next coefficient.Add these two values together and write the result under the next coefficient. Repeat this process until you've reached the constant term.Write the final result as the quotient and the last value as the remainder.

In this case, the quotient is[tex]9x^3 + 4x^2 + 5x + 2[/tex].

Related Questions

The general form of the equation of a circle is x2 + y2 + 8x + 22y + 37 = 0.
The equation of this circle in standard form is

HELP WILL MEDAL,

Answers

The standard form of the equation for a circle is (x-a)^2 + (y-b)^2 = r^2 where (a,b) = center of circle r = radius. So let's do it. x^2 + y^2 + 8x + 22y + 37 = 0 Let's start with determining a. We know that (x-a)^2 will result in an x^2 term and an 8x term. Let's square (x-a) and we get x^2 - 2ax + a^2. The x^2 term is OK and we have 8x = -2ax So 8x = -2ax 8 = -2a -4 = a So we now know that part of the equation will be (x - -4)^2 = (x + 4)^2. Let's expand that, giving x^2 + 8x + 16 and since we're adding 16 to the left, we need to add that to the right as well. So our equation becomes (x + 4)^2 + y^2 + 22y + 37 = 16 Now let's work on the y terms. Using the same logic as above the equation to solve is 22y = -2by 22 = -2b -11 = b So (y - -11)^2 = (y+11)^2. And expanding gives us y^2 + 22y + 121 which means we need to add 121 to the right, so we have (x + 4)^2 + (y + 11)^2 + 37 = 16 + 121 (x + 4)^2 + (y + 11)^2 + 37 = 137 (x + 4)^2 + (y + 11)^2 = 100 And a simple rewrite of the right hand side gives us (x + 4)^2 + (y + 11)^2 = 10^2 So the final equation is (x + 4)^2 + (y + 11)^2 = 10^2 Which indicates a circle with a radius of 10 centered at (-4,-11)

sin A=0.7245
A=

sin D=0.4567
D=

Answers

The simplest way would be to use a calculator to evaluate B = arcsin(0.7245)

If you don't have a calculator, the next, more complex way would be to interpolate a table of sines and find the value of the angle whose sine is 0.7245. That is the method that was most widely used before the invention of hand held calculators and after sine tables had been published.

The next, most complex way would be to evaluate terms in the infinite series representation of the arcsine function which is the way the sine tables were developed for publication. That series is
arcsin(x) = x + x³/6 + (3/40)x^5 + (15/336)x^7 + ...

The result for any of those methods would be B = 46.4°

Geometrically, you could:
1) Draw a circle of known radius, R. centered at the origin of a rectangular coordinate system
2) Draw a line parallel to the x axis a distance 0.7245R above the x-axis
3) Draw a line connecting the origin to the rightmost point of intersection between the circle 1) and the line 2).
4) Measure the angle between the line 3) and the +x axis.

The Angle 4) will be the measure of the angle whose sine is 0.7245.

That explains four ways you can find the measure of the angle whose sine is 0.7245.

Hurry please I need the answer right away soo send me math work answers my friend said it's 42? Is it right

Answers

1/2*12*7=1/2*84=42

Hope i helped :)

The area of a rectangle is 10r (squared) − 11r − 6. The width is 2r − 3. What is the length?

Answers

10r^2 − 11r − 6 = (2r - 3)(5r +2)
so
A = (2r - 3)(5r +2)
as you know A = L * W
if width = (2r - 3) then length = (5r +2)

answer
length = (5r +2)

The length of the rectangle whose area is (10r² − 11r − 6) and the width is (2r−3) is (5r+2).

What is a rectangle?

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but reverse statement may or may not be true.

Area of rectangel = Length × Width

Given that the area of a rectangle is 10r² − 11r − 6, while the width is 2r − 3. Therefore, it can be writen as,

[tex]\text{Area = Length}\times\text{Width}\\\\10r^2 - 11r - 6 = \text{Length} \times (2r - 3)\\\\\text{Length} = \dfrac{10r^2 - 11r - 6}{2r-3}\\\\\text{Length} = 5r+2[/tex]

Hence, the length of the rectangle is (5r+2).

Learn more about Rectangle:

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You have 20 shirts in your closet. 4 blue, 7 red, 3 green and 6 black. You pick one without looking. What is the probability that you pick a blue or black shirt?

Answers

50% /// because if it is blue+black (6+4=10) and the leftovers 3+7=10 and if there is 20 shirts and its 10 and 10 its half so half is 50%

Please help with this one question thanks!

Answers

A 240 is the correct answer

The main tank at an aquarium is a cylinder with a diameter of 203 ft and a height of 4 ft. What is its approximate volume? Use 3.14 for π. a. 129,400 ft3 b. 79,830 ft3 c. 236,560 ft3 d. 32,366 ft3

Answers

V=pi *r^2* h
diameter d= 2r=203
r=203/2=101.50
h=4
V=3.14 * 4 * (101.50)^2
V=129,400 ft^3

Answer: [tex]a.\ 129,400\ ft^3[/tex]

Step-by-step explanation:

The volume of a cylinder is given by:-

[tex]\text{Volume}=\pi r^2h[/tex]

Given: The diameter of cylinder = 203 ft.

Then the radius of the cylinder =[tex]\dfrac{203}{2}[/tex] ft.

The height of the cylinder = 4 ft.

Now, The volume of cylinder :will be -

[tex]\text{Volume}=(3.14)(\dfrac{203}{2})^2(4)=\\\\\Rightarrow\text{Volume}=129,396.26\approx129,400\ ft^3[/tex]

how can you eliminate fraction from each side of the equation to make finding the solution easier 1/2(x-4)=1/3x+2

Answers

Multiply by the product of the denominators. Here, that is 2*3 = 6.

___
The above approach always works. You likely have been told to multiply by the least common denominator, which in this case is the same thing.

If you don't take the trouble to find the least common denominator, at some point you will be factoring out a common factor. (You may be doing that anyway.)

1/2(x-4)=1/3x+2
3(x -4) = 2x +12
x = 24

Adeeb bought 5 oranges and 15 apples from the farmer's market. The equation 5r+15a=10.5 represents the amount of money he spent. Faye bought 12 oranges and 11 apples, represented by the equation 12r+11a=11.45 . What was the cost of each apple

Answers

cost of an orange = r
cost of an apple = a

Adeeb bought;
amount of oranges - 5
amount of apples = 15
the equation for the amount he spent
5r + 15a = 10.5

Faye bought
oranges - 12
apples - 11
the equation for the amount he spent
12r + 11a = 11.45
set of simultaneous equation
5r + 15a = 10.5 ---> 1)
12r + 11a = 11.45 ---> 2)
divide by the first equation by 5
r + 3a = 2.1--> 3)
Multiply third by 12
12r + 36a = 25.2 ---> 4)
subtract 2nd equation from the 4th
25a = 13.75
a = 0.55
substituting a = 0.55 in 3rd equation
r + 3*0.55 = 2.1
r = 2.1 - 1.65
r = 0.45
price of an orange = 0.45
price of an apple = 0.55

The owner of a shop bought a scarf at the wholesale price of $8.00 and marked it up by 300%. What is the selling price?

Answers

The owner of the shop who bought a scarf for $8.00 is now selling it for $24.00.

The selling price would equal $24

Jake is in the stands at a football game with his girlfriend Diane. He decides that he needs to ask Diane a serious question, so he brings her to a quiet lounge in the stadium complex. What type of context has Jake changed?

A. the cultural context
B. the social-psychological context
C. the temporal context,

Answers

Jake has opted for the social psychological context. Jake has a serious question for Diane and he wants to take her to a quiet and pleasant surrounding in order to answer the question. One might think that Jake is going to ask Diane to marry him. Yet that would be jumping to conclusions, which is something that is difficult at times. One doesn't know the question and it can't be inferred. He simply wants to ask her something removed from crowded bleachers with cheering fans.

Jake has shifted the (B) social-psychological context by moving to a quieter, more private space in the stadium to ask Diane a serious question, which changes the norms and atmosphere to match the situation's gravity.

Jake has changed the social-psychological context by moving from the stands to a quiet lounge. The social-psychological dimension of context includes status relationships among participants, roles, norms of the society or group, and the overall atmosphere like friendliness, formality, or gravity of the situation. By choosing to ask Diane a serious question in a quieter, more private environment, Jake is altering the norms and atmosphere to better suit the gravity of the conversation he intends to have, thus changing the social-psychological context.

The Smiths were just approved for a 25 year mortgage at an 11% fixed rate. If they had not filed bankruptcy in the past, they could have gotten a rate of 7%. If their loan amount is $128,000, how much more per month will the Smiths be paying for their mortgage as a result of their bankruptcy? a. $349.86 b. $125,840.78 c. $904.68 d. $235.09

Answers

To answer the problem, the amortization formula will be of great help. The formula is as follows:

A = P × ((r(1+r)ⁿ)/((1+r)ⁿ-1))
A = is the amortization
P = is the principal
r = is the rate
n = is the period

1. Compute for the amortization using the 11% interest rate.

A = $128000 × ((0.11(1.11)²⁵)/((1.11)²⁵-1))
= $1,254.54
*if solve manually, the answer should be divided by 12 because it was on a monthly basis.

2. Compute for the amortization using the 7% interest rate.

A = $128000 × ((0.07(1.07)²⁵)/((1.07)²⁵-1))
= $904.68
*if solve manually, the answer should be divided by 12 because it was on a monthly basis.

3. Thus, the increase in monthly amortization as a result of higher interest rate is $349.86.

so your answer is A ;)

solve the equation x-5=15 and state Euclid's axiom used

Answers

[tex]x-5 = 15[/tex]
[tex]x = 15 + 5[/tex]
[tex]x=20[/tex]

If equals are added to equals, the the remainders are equal.

Hope this helps !

Photon

Describe the trend in the scatter plot.

not enough information because the trend line is unclear

positive correlation

no correlation

negative correlation

Answers

The correct answer is C. no correlation

Answer:

No correlation.

Step-by-step explanation:

A Scatter (XY) Plot has points that show the relationship between two variables.

Scatter plots use a collection of points placed using Cartesian coordinates to show values of two variables. By showing a variable on each axis, it can be detected if there is a relationship or correlation between the two variables.

Several types of correlation can be interpreted through the patterns shown in the scatter diagrams. These are: positive (values increase together), negative (one value decreases as the other increases), null (no correlation).

In the case presented, it can be clearly seen that the variables have no correlation, because the trend is not that the points form a straight line, but that there is too much dispersion.

So, the answer is:

No correlation.

Hope this helps!

Please help with 2 questions thank you.

Answers

1) m∠1 = 360°/8 = 45° . . . . . a regular octagon is 8-way rotationally symmetrical, so each sector is 1/8 of a circle.

2) m∠2 = (180° -45°)/2 = 67.5° . . . . . . the angles of a triangle add to 180°. The base angles of an isosceles triangle are equal.

Regular Polygons multiple choice
I think it's a - 60 but I'm not sure

Answers

Yes you are correct. An equilateral triangle would combine with the dodecagon (12 sided polygon) and the square to help tessellate the plane.

PLEASE HELPME QUICKLY QUICK

Answers

Okay. So no more than 660 minutes will be spent cutting the lawn. The sign will be less than or equal to. A and D are out, because those show greater than or equal to symbols, which is not what we're looking for. x represents the number of lawns mowed, which is an average of 40 minutes, and he will have done 110 minutes. The equation is 40x + 110 ≤ 660. The answer is C.

What is a possible value for the missing term of the Geometric sequence. 50_450

Answers

Let the missing number be x
r= x/50= 450/x
x^2 = 22500
x = 150

Answer: The missing term of the Geometric sequence can be 150.

Step-by-step explanation:

Let the missing number is x,

Hence, the G.P. will,

50, x, 450

Since, the consecutive element of G.P. are in same ratio,

[tex]\implies \frac{x}{50}= \frac{450}{x}[/tex]

[tex]\implies x^2 = 50\times 450 = 22500[/tex]

[tex]\implies x = 150[/tex]

Thus, the missing term of the Geometric sequence can be 150.

How many points did the team score in the 11th game and why?

Answers

The team's point total after 10 games was 10*35 = 350.
The team's point total after 11 games was 11*33 = 363.
The team scored 13 points in game 11.

sam decides to build a square garden if the area of the other garden is 9x^2 -24x +16 square feet what is the length of one side of the garden

Answers

9x^2 -24x +16 can be factored into (3x-4)²
the length of each side is 3x-4

5x2=5x^2 4x2+4x^2
1. What values of a, b, and c would you use in the quadratic formula for the following equation? 5x2+9x=4

2. attachment

3. What are the approximate solutions of 2x2-x+10=0?

4. Solve the equation using the quadric formula. 4x2+3x-10=0

5. Solve the equation using the quadric formula. -x2+27=6x

6. Which method is the best method for solving the equation? 8x2-13x+3=0

7. How many solutions are there for 5x2+7x-4=0?

8. The perimeter of a rectangle is 54 cm. The area of the same rectangle is 176 cm2. What are the dimensions of the rectangle?

Answers

1.) a=5, b=9, c=-4
2.) C
3.) No solution
4.) x=-2, x=1.25
5.) x=-9, x=3
6.) quadratic formula
7.) 2
8.) 11cm by 16cm

100% for The Quadratic Formula and the Discriminant practice

1. The equation 5x^2+9x=4, can be rewritten as 5x^2+9x-4=0, where a=5 (the coefficient of the quadratic term), b = 9 (the coefficient of the linear term) and c = -4 (the independent term).

2. No attachment is shown.

3. To use the quadratic formula, the coefficients are: a = 2, b = -1 and c = 10. However, the discriminant, i. e., b^2 -4(a)(c) is negative, therefore, there is no real solution.

4. You have to use the quadratic formula, with a = 4, b = 3 and c = -10, as follows:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)} [/tex]

[tex]x = \frac{-3 \pm \sqrt{3^2 - 4(4)(-10)}}{2(4)} [/tex]

[tex]x = \frac{-3 \pm \sqrt{169}}{8} [/tex]

[tex]x_1 = \frac{-3 + 13}{8} [/tex]

[tex]x_1 = \frac{5}{4} [/tex]

[tex]x_2 = \frac{-3 - 13}{8} [/tex]

[tex]x_2 = -2 [/tex]

5. Rewriting the formula, so that all the terms are on one side and ordering the polynomial expression, gives: -x2-6x+27=0. Here a = -1, b = -6 and c = 27. Using the quadratic formula gives

[tex]x = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)} [/tex]

[tex]x = \frac{6 \pm \sqrt{6^2 - 4(-1)(27)}}{2(-1)} [/tex]

[tex]x = \frac{6 \pm \sqrt{144}}{-2} [/tex]

[tex]x_1 = \frac{6 + 12}{-2} [/tex]

[tex]x_1 = -9 [/tex]

[tex]x_2 = \frac{6 - 12}{-2} [/tex]

[tex]x_2 = 3 [/tex]

6. When the second grade polynomial has all of its coefficients (a, b and c) different than zero, like this case, the best method for solving the equation is the quadratic formula .

7. When the discriminant is greater than zero, there are two different solutions and when it is equal to zero, it has one double solution.

The discriminant for this case is 7^2 - 4(5)(-4) = 129. So, there are two different solutions .

8. Let's call the sides of the rectangle a and b.

perimeter formula: 2a + 2b = 54 cm (eq. 1)

area formula: (a)(b) = 176 cm2 (eq. 2)

Isolating a in equation 1, gives (units are omitted):

2a + 2b = 54

2a = 54 - 2b

a = 27 - b (eq. 3)

Replacing equation 3 into equation 2, gives (units are omitted):

(a)(b) = 176

(27 - b)(b) = 176

-b^2 + 27b - 176 = 0

Using quadratic formula, we get

[tex]x = \frac{-27 \pm \sqrt{27^2 - 4(-1)(-176)}}{2(-1)} [/tex]

[tex]x = \frac{-27 \pm \sqrt{25}}{-2} [/tex]

[tex]x_1 = \frac{-27 + 5}{-2} [/tex]

[tex]x_1 = 11 [/tex]

[tex]x_2 = \frac{-27 - 5}{-2} [/tex]

[tex]x_2 = 16 [/tex]

Then, there are two possible values for b, 11 cm and 16 cm. Replacing these values into equation 3 gives:

a = 27 - 11 = 16 cm

a = 27 - 16 = 11 cm

Therefore, the two sides are 11 cm and 16 cm long, despite their names.

MEDAL
True or false

The coefficient of x^k y^n-k in the expansion of (x+y)^n equals (n-k / k),

Answers

The statement The coefficient of x^k y^n-k in the expansion of (x+y)^n equals (n-k / k) is true. This will show the standard formula and the expansion of it. We all know that it can still be expanded based on the power or degree of the terms.

Answer: the answer is FALSE. Just took this on a p e x

Step-by-step explanation:

what is the factored form of 3c²+24c+48 ?

Answers

1st step factor 3 out of each number in the equation to get:

3(c^2+8c+16)

16 can be rewritten as 4^2 to get:
3(c^2+8c+4^2)

4+4 = 8 ( the middle number)

so the factor would be 3(c+4)^2

25, 8, 10, 35, 5, 45, 40, 30, 20 What is the upper quartile of the data set above?A.35
B. 37.5
C. 37
D. 40,

Answers

An upper quartile is the range of numbers above the median in a set. Thus, the numbers have to be rearranged mentally or on paper. Fortunately, there are an odd set of numbers, so one number, 25, is the median. The upper quartile is 30, 35, 40, 45.

Please help! How many ways can a cook arrange 7 or 10 spice jars on a spice rack?

A. 720
B. 604,800
C. 5,040
D. 120

Answers

i think its C.or A. Im not sure

A will be your answer

(ab - 9)(ab + 8) Please help

Answers

Use FOIL. :)

(ab - 9)(ab + 8)
ab^2 + 8ab - 9ab + 72
Simplify:
ab^2 - ab - 72

a^2 b^2 + 8ab - 9ab - 72
a^2 b^2 + (8ab - 9ab) - 72
[tex] a^{2} [/tex] [tex] b^{2} [/tex] - ab - 72

-Love, live, and watch anime.

The value of x is
PLEASE ANSWER FAST IM IN THE MIDDLE OF A TEST

Answers

The value of the exterior angle next to a triangle is equal to the sum of two angles of the triangle, opposite of the interior angle. In this case: Angle QRT is equal to the sum of angle RTS and angle RST. So if we put that into an equation it will look like this:

9x = 5x + (9 + x)
Now we can solve for x.
9x = 5x + 9 + x
9x = 6x + 9 (Combine like terms)
9x - 6x = 9 (transpose)
3x = 9
3x/3 = 9/3

x = 3

Name the sets of numbers to which -1/2 belongs

A.integers,rational numbers
B.whole numbers,natural numbers, integers
C.whole numbers,integers,rational numbers
D.rational numbers

Answers

A Hope Fully Im Right / Im pretty sure thats the answer

What is the square root of 64y^16?

Answers

[tex] \sqrt{64y^{16}}= \sqrt{(8y^{8})^2}=8y^8[/tex]

The square root of the given algebraic expression [tex]64y^{16}[/tex] is [tex]\bold{8y^8}[/tex]

What is an algebraic expression?

"It is a mathematical statement which consists of numbers, variables and mathematical operations."

For given question,

We have been given an algebraic expression [tex]64y^{16}[/tex]

We need to find the square root of given algebraic expression.

[tex]\Rightarrow \sqrt{ 64y^{16}}\\\\= \sqrt{ 64\times y^{16}} \\\\=\sqrt{64} \times \sqrt{y^{16}} \\\\=8\times (y^{16})^{\frac{1}{2} }\\\\=8\times y^{\frac{16}{2} }\\\\= 8\times y^8[/tex]

Therefore, the square root of the given algebraic expression [tex]64y^{16}[/tex] is [tex]\bold{8y^8}[/tex]

Learn more about the algebraic expression here:

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How many solutions does the equation sin(4x)=1/2 have on the interval (0,2pi)?

Answers

8 I believe let me know if I am wrong

Answer:

2 solutions

Step-by-step explanation:

Given the equation sin(4x)=1/2, to know the total number of solutions that the equation has within the interval (0,2π), we will need to solve for x first.

sin(4x)=1/2

4x = arcsin1/2

4x = 30°

x = 30/4

x1 = 7.5° (This angle lies in the first quadrant)

Since sine is positive in the second quadrant as well and the angle in the second quadrant is (180°-theta) where theta is 7.5°, therefore;

x2 = 180-7.5°

x2 = 172.5°

Therefore 7.5° and 172.5° are the two solutions of x that falls within the range (0,2π)

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