question

What is the greatest common factor of the terms in the polynomial 3x³ - 3x² - 18x???(FPC)

answer

3x

question

What is the greatest common factor of the terms in the polynomial 8x? - 4x³ - 18x²?

answer

2x²

question

Which product of prime polynomials is equivalent to 8x? + 36x³ - 72x²?

answer

4x²(2x - 3)(x + 6)

question

What is the greatest common factor of the terms in the polynomial 12x? + 27x³ + 6x²?

answer

3x²

question

5x³ + 20x² + 2x + 8
5x²(x + 4) + 2(x + 4)
Which is the completely factored form of his polynomial?

answer

(5x² + 2) (x + 4)

question

Which product of prime polynomials is equivalent to 8x³ - 2x?

answer

2x(2x + 1)(2x - 1)

question

7x³ - 21x² + 5x - 15
7x²(x - 3) + 5(x -3)
Which is the completely factored form of her polynomial?

answer

(7x² + 5) (x - 3)

question

12x? + 30x³ + 4x² + 10x
Ax(Bx² + 1) (2x + 5)
B=[___________]

answer

3

question

Which is the completely factored form of 4x³ + 10x² - 6x?

answer

2x(x + 3)(2x - 1)

question

Which is the completely factored form of 12x³ - 60x² + 4x - 20?

answer

4(3x² + 1)(x - 5)

question

Which product of prime polynomials is equivalent to 3x? - 81x?

answer

3x(x - 3)(x² + 3x + 9)

question

What is the greatest common factor of the terms in the polynomial 4x? - 32x³ - 60x²?

answer

4x²

question

3x? - 18x³ + 9x² -54x
Ax(x² + B) (x + C)
C=[___________]

answer

-6

question

Which is the completely factored form of 3x² - 12x - 15?

answer

3(x + 1)(x - 5)

question

What is the greatest common factor of the terms in the polynomial 12x? + 27x³ + 6x²?

answer

3x²

question

Which polynomial is prime?

answer

2x + 9

question

4x³ + 12x² + 5x + 15
4x²(x + 3) + 5(x + 3)
Which is the completely factored form of her polynomial?

answer

(4x2 + 5)(x + 3)

question

Which polynomial is prime?

answer

x² + 6

question

The long division below shows the first term of the quotient. Which polynomial should be subtracted from the dividend first?
. . . .____x²____
x+2|x³+3x²+x??(DoP)

answer

x³ + 2x²

question

What is the quotient (x³ + 6x² + 11x + 6) ÷ (x² + 4x + 3)?

answer

x + 2

question

The quotient of (x? - 3x³ - 3x² - 10x + 15) and a polynomial is (x² - 5). What is the polynomial?

answer

x³ + 2x - 3

question

What is the quotient of the following division problem?
. . . ._____x+2
x+1|x²+3x+2
. . . .____x²+x
. . . .0+2x+2
. . . .___2x+2
. . . . . . . . 0

answer

x² + 3x + 2

question

What is the remainder of the following division problem?
. .___1
x|x+1
. .x___
. .0+1

answer

1

question

What is the first term of the quotient of the following division problem?
(x³ - 1) ÷ (x + 2)

answer

x²

question

What is the quotient (x³ + 8) ÷ (x + 2)?

answer

x² - 2x + 4

question

What is the first step of the following division problem?
(8x³ - x² + 6x + 7) ÷ (2x - 1)

answer

Divide 8x³ by 2x.

question

What is the quotient of (x³ + 3x² - 4x - 12) / (x² + 5x + 6)?
[_________]

answer

x - 2

question

What is the quotient (x³ - 3x² + 5x - 3) ÷ (x - 1)?

answer

x² - 2x + 3

question

If (x2 - 4) ÷ (x + 2) = x - 2, which polynomial should fill in the blank below?
(x + 2) ´ ______ = x2 - 4

answer

x - 2

question

What is the quotient (3x4 - 4x2 + 8x - 1) ÷ (x - 2)?

answer

3x³ + 6x² + 8x + 24 + 47/x-2

question

The quotient of (x? + 5x³ - 3x - 15) and a polynomial is (x³ - 3). What is the polynomial?

answer

x + 5

question

What is the quotient (125 - 8x³) ÷ (25 + 10x + 4x²)?

answer

-2x + 5

question

One factor of f(x) = 5x³ + 5x² - 170x + 280 is (x + 7). What are all the roots of the function? Use the Remainder Theorem.??(SD&tRT)

answer

x = -4, x = -2, or x = 7
_x = -7, x = 2, or x = 4
x = -7, x = 5, or x = 280
x = -280, x = -5, or x = 7

question

Use synthetic division to solve (x³ + 1) ÷ (x - 1). What is the quotient?

answer

x³ - x² + x

question

One factor of f(x) = 4x³ - 4x² - 16x + 16 is (x - 2). What are all the roots of the function? Use the Remainder Theorem.

answer

x = 1, x = 2, or x = 4
_x = -2, x = 1, or x = 2
x = 2, x = 4, or x = 16
x = -16, x = 2, or x = 16

question

One root of f(x) = x³ - 4x² - 20x + 48 is x = 6. What are all the factors of the function? Use the Remainder Theorem.

answer

(x - 2)(x + 4)(x - 6)

question

Use synthetic division to solve (3x? + 6x³ + 2x² + 9x + 10) / (x - 2). What is the quotient?

answer

3x³ + 12x² + 26x + 61 + 132/x + 2
_3x³ + 2x + 5
3x³ + 12x² + 26x + 61 + 132/x - 2
3x? + 2x² + 5x

question

The volume of a rectangular prism is 2x³ + 9x² - 8x - 36 with height x + 2. Using synthetic division, what is the area of the base?

answer

2x² + 5x - 18

question

Use synthetic division to solve (2x³ + 4x² - 35x + 15) / (x - 3). What is the quotient?

answer

2x² + 10x -5

question

Use synthetic division to solve (4x³ - 3x² + 5x + 6) / (x + 6). What is the quotient?

answer

4x² - 27x + 167 - 996/x - 6
4x² + 21x + 131 + 792/x + 6
4x² + 21x + 131 + 792/x - 6
_4x² - 27x + 167 - 996/x + 6

question

What divisor is represented by the synthetic division below?
-5|2 10 1 5
. . |_-10 0-5
. . .2 .0 .1 0

answer

5
_x + 5
x - 5

question

The volume of a rectangular prism is (x3 - 3x2 + 5x - 3), and the area of its base is (x2 - 2). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?

answer

x-3 + 7x-9/x²-2

question

If (x + 8) is a factor of f(x), which of the following must be true?

answer

f(-8) = 0

question

What dividend is represented by the synthetic division below?
-5|2 10 1 5
. . |_-10 0-5
. . .2 .0 .1 0

answer

2x³ + 10x² + x + 5

question

If f(1) = 0, what are all the roots of the function x³ + 3x² - x - 3? Use the Remainder Theorem.

answer

x = -3, x = -1, or x = 1

question

If -1 is a root of f(x), which of the following must be true?

answer

A factor of f(x) is (x + 1).

question

One root of f(x) = x³ - 9x² + 26x - 24 is x = 2. What are all the roots of the function? Use the Remainder Theorem.

answer

x = 2, x = 3, or x = 4

question

The area of a rectangle is 5x³ + 19x² + 6x - 18 with length x + 3. Using synthetic division, what is the width of the rectangle?

answer

5x² + 4x - 6

question

According to the Rational Root Theorem, which statement about f(x) = 12x³ - 5x² + 6x + 9???

answer

Any rational root of f(x) is a multiple of 12 divided by a multiple of 9.
Any rational root of f(x) is a multiple of 9 divided by a multiple of 12.
_Any rational root of f(x) is a factor of 9 divided by a factor of 12.

question

What is the completely factored form of f(x) = x3 - 2x2 - 5x + 6?

answer

f(x) = (x + 2)(x - 3)(x + 6)
f(x) = (x + 2)(x - 3)(x - 6)
f(x) = (x - 2)(x + 3)(x - 1)
_f(x) = (x + 2)(x - 3)(x - 1)

question

According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 - 2x4 + 9x3 - x2 + 12?

answer

f(x) = 3x5 - 2x4 - 9x3 + x2 - 12

question

According to the Rational Root Theorem, which could be a factor of the polynomial f(x) = 6x4 - 21x3 - 4x2 + 24x - 35?

answer

2x - 7

question

According to the Rational Root Theorem, the following are potential roots of f(x) = 2x2 + 2x - 24.
-4, -3, 2, 3, 4
Which are actual roots of f(x)?

answer

_-4 and 3
-4, 2, and 3
-3 and 4
-3, 2, and 4

question

According to the Rational Root Theorem, which number is a potential root of f(x) = 9x8 + 9x6 - 12x + 7?

answer

7/3

question

The graph of f(x) = x6 - 2x4 - 5x2 + 6 is shown below.
How many roots of f(x) are rational numbers? (Roots: -183/250, -1, 1, 183/250)

answer

2

question

The polynomial function f(x) = 10x6 + 7x - 7 is graphed below.
According to the rational roots theorem, which is a possible root at point P?

answer

The root at point P may be 7/10.

question

According to the Rational Roots Theorem, which statement about f(x) = 25x7 - x6 - 5x4 + x - 49 is true?

answer

Any rational root of f(x) is a factor of -49 divided by a factor of 25.

question

According to the Rational Root Theorem, which statement about f(x) = 66x4 - 2x3 + 11x2 + 35 is true?

answer

Any rational root of f(x) is a factor of 35 divided by a factor of 66.

question

Using the Rational Root Theorem, what are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x - 12?

answer

-4/5 and 3/4

question

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 9x4 - 2x2 - 3x + 4?

answer

±1/9, ±2/9, ±1/3, ±4/9, ±2/3, ±1, ±4/3, ±2, ±4

question

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 15x11 - 6x8 + x3 - 4x + 3?

answer

±1/15, ±1/5, ±1/3, ±3/5, ±1, ±3

question

According to the Rational Root Theorem, -7/8 is a potential rational root of which function?

answer

f(x) = 24x7 + 3x6 + 4x3 - x - 28

question

According to the Rational Root Theorem, the following are potential roots of f(x) = 60x² - 57x - 18.

answer

-1/4

question

How many roots of f(x) are rational numbers? (Roots: 2, 3, 9/2)

answer

3

question

What are the solutions of the equation x4 + 95x2 - 500 = 0? Use factoring to solve.??

answer

x = ±?5 and x = ±10i

question

Which equation is quadratic in form?

answer

_x6 + 6x4 + 8 = 0
7x6 + 36x3 + 5 = 0
4x9 + 20x3 + 25 = 0

question

Which quadratic equation is equivalent to (x2 - 1)2 - 11(x2 - 1) + 24 = 0?

answer

u2 - 11u + 24 = 0 where u = (x2 - 1)

question

What are the solutions of the quadratic equation (x - 8)2 - 13(x - 8) + 30 = 0? Use u substitution to solve.

answer

x = -11 and x = -18
x = -2 and x = 5
x = 2 and x = -5
_x = 11 and x = 18

question

What are the solutions of the equation x4 + 3x2 + 2 = 0? Use u substitution to solve.

answer

x = ±i?2 and x = ±i

question

Which quadratic equation is equivalent to (x + 2)2 + 5(x + 2) - 6 = 0?

answer

(u + 2)2 + 5(u + 2) - 6 = 0 where u = (x - 2)
u2 + 4 + 5u - 6 = 0 where u = (x - 2)
_u2 + 5u - 6 = 0 where u = (x + 2)
u2 + u - 6 = 0 where u = (x + 2)

question

What substitution should be used to rewrite 4x4 - 21x2 + 20 = 0 as a quadratic equation?

answer

u = x²

question

Which equation is quadratic in form?

answer

_4(x - 2)2 + 3x - 2 + 1 = 0
8x5 + 4x3 + 1 = 0
10x8 + 7x4 + 1 = 0
9x16 + 6x4 + 1 = 0

question

What is the solution of the equation (x - 5)2 + 3(x - 5) + 9 = 0? Use u substitution and the quadratic formula to solve.

answer

x = -3±3i?3/2
_x = 7±3i?3/2
x = 2
x = 8

question

What are the solutions of the equation x6 - 9x3 + 8 = 0? Use u substitution to solve.

answer

x = 1 and x = 2

question

What are the solutions of the equation x4 - 5x2 - 14 = 0? Use factoring to solve.

answer

x = ± ?7 and x = ± ?2
x = ±i?7 and x = ±i?2
x = ±i?7 and x = ± ?2
_x = ± ?7 and x = ±i?2

question

What substitution should be used to rewrite 4x12 - 5x6 - 14 = 0 as a quadratic equation?

answer

u = x?

question

Which quadratic equation is equivalent to (x - 4)2 - (x - 4) - 6 = 0?

answer

u2 - u - 6 = 0 where u = (x - 4)

question

What substitution should be used to rewrite 6(x + 5)2 + 5(x + 5) - 4 = 0 as a quadratic equation?

answer

u = (x + 5)

question

What are the solutions of the equation x6 + 6x3 + 5 = 0? Use factoring to solve.

answer

x = -³?5 and x = -1

question

Let a and b be real numbers where a ? b ? 0. Which of the following functions could represent the graph below?
. .. . | . /
____/|/____
. . . . .|
. . . . .|??

answer

f(x) = (x - a)²(x - b)?

question

Which statement describes the graph of f(x) = 4x? + 40x? + 100x??

answer

The graph crosses the x axis at x = 0 and touches the x axis at x = -5.

question

Which statement describes the graph of f(x) = -x4 + 3x3 + 10x2?

answer

The graph touches the x axis at x = 0 and crosses the x axis at x = 5 and x = -2.

question

Which of the following graphs could be the graph of the function f(x) = -0.08x(x² - 11x + 18)?

answer

. . . . . .|
. . . . . . | . ./
_________|__/_____
. . . . . . . |. . . . . .|
. . . . . . . |. . . . . .|
. . . . . . . |. . . . . .|

question

At which root does the graph of f(x) = (x - 5)³(x + 2)² touch the x axis?

answer

-2

question

What is the end behavior of the graph of the polynomial function f(x) = 3x6 + 30x5 + 75x4?

answer

As x ? -?, y ? -? and as x ? ?, y ? -?.
As x ? -?, y ? -? and as x ? ?, y ? ?.
As x ? -?, y ? ? and as x ? ?, y ? -?.
_As x ? -?, y ? ? and as x ? ?, y ? ?.

question

At which root does the graph of f(x) = (x + 4)6(x + 7)5 cross the x axis?

answer

-7

question

A polynomial function has a root of -5 with multiplicity 3, a root of 1 with multiplicity 2, and a root of 3 with multiplicity 7. If the function has a negative leading coefficient and is of even degree, which statement about the graph is true?

answer

The graph of the function is negative on (3, ?).

question

Which of the following graphs could be the graph of the function 0.03x²(x² - 25)?

answer

. . . .|. . . .|. . . .|
. . . .|. . . .|. . . .|
______|_____|_____|______
. . . . .__/|__/
. . . . . . . . |
. . . . . . . . |

question

Which statement describes the graph of f(x) = -4x³ - 28x² - 32x + 64?

answer

The graph touches the x axis at x = -4 and crosses the x axis at x = 1.

question

Which graph shows the end behavior of the graph of f(x) = 2x? - 2x² - 5?

answer

. . . .|. . . . |. . . .|
. . . . |. . . .|. . . |
_________/|__/_______
. . . . . . . . |
. . . . . . . . |
. . . . . . . . |

question

Which graph has the same end behavior as the graph of f(x) = -3x³ - x² + 1?

answer

. .|. . . . . . .|
. . | . . . . . |
__________/|___________
. . . .__/. .|. .
. . . . . . . . |. . .|
. . . . . . . . |. . . |

question

At which root does the graph of f(x) = (x - 5)³(x + 2)² touch the x axis?

answer

-2

question

Which of the following graphs could be the graph of the function f(x) = x? + x³ - x² - x?

answer

. . . . . . .|. |. . .|
. . . . . . .| .|. . .|
___________-|___/________
. . . . . . . . |.-
. . . . . . . . |