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

What is the greatest common factor of the terms in the polynomial 8x⁴ – 4x³ – 18x²? |
2x² |

Which product of prime polynomials is equivalent to 8x⁴ + 36x³ – 72x²? |
4x²(2x – 3)(x + 6) |

What is the greatest common factor of the terms in the polynomial 12x⁴ + 27x³ + 6x²? |
3x² |

5x³ + 20x² + 2x + 8 |
(5x² + 2) (x + 4) |

Which product of prime polynomials is equivalent to 8x³ – 2x? |
2x(2x + 1)(2x – 1) |

7x³ – 21x² + 5x – 15 |
(7x² + 5) (x – 3) |

12x⁴ + 30x³ + 4x² + 10x |
3 |

Which is the completely factored form of 4x³ + 10x² – 6x? |
2x(x + 3)(2x – 1) |

Which is the completely factored form of 12x³ – 60x² + 4x – 20? |
4(3x² + 1)(x – 5) |

Which product of prime polynomials is equivalent to 3x⁴ – 81x? |
3x(x – 3)(x² + 3x + 9) |

What is the greatest common factor of the terms in the polynomial 4x⁴ – 32x³ – 60x²? |
4x² |

3x⁴ – 18x³ + 9x² -54x |
-6 |

Which is the completely factored form of 3x² – 12x – 15? |
3(x + 1)(x – 5) |

What is the greatest common factor of the terms in the polynomial 12x⁴ + 27x³ + 6x²? |
3x² |

Which polynomial is prime? |
2x + 9 |

4x³ + 12x² + 5x + 15 |
(4×2 + 5)(x + 3) |

Which polynomial is prime? |
x² + 6 |

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

What is the quotient (x³ + 6x² + 11x + 6) ÷ (x² + 4x + 3)? |
x + 2 |

The quotient of (x⁵ – 3x³ – 3x² – 10x + 15) and a polynomial is (x² – 5). What is the polynomial? |
x³ + 2x – 3 |

What is the quotient of the following division problem? |
x² + 3x + 2 |

What is the remainder of the following division problem? |
1 |

What is the first term of the quotient of the following division problem? |
x² |

What is the quotient (x³ + 8) ÷ (x + 2)? |
x² – 2x + 4 |

What is the first step of the following division problem? |
Divide 8x³ by 2x. |

What is the quotient of (x³ + 3x² – 4x – 12) / (x² + 5x + 6)? |
x – 2 |

What is the quotient (x³ – 3x² + 5x – 3) ÷ (x – 1)? |
x² – 2x + 3 |

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

What is the quotient (3×4 – 4×2 + 8x – 1) ÷ (x – 2)? |
3x³ + 6x² + 8x + 24 + 47/x-2 |

The quotient of (x⁴ + 5x³ – 3x – 15) and a polynomial is (x³ – 3). What is the polynomial? |
x + 5 |

What is the quotient (125 – 8x³) ÷ (25 + 10x + 4x²)? |
-2x + 5 |

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) |
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 |

What remainder is represented by the synthetic division below? |
0 |

Use synthetic division to solve (x³ + 1) ÷ (x – 1). What is the quotient? |
x³ – x² + x |

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

One root of f(x) = x³ – 4x² – 20x + 48 is x = 6. What are all the factors of the function? Use the Remainder Theorem. |
(x – 2)(x + 4)(x – 6) |

Use synthetic division to solve (3x⁴ + 6x³ + 2x² + 9x + 10) / (x – 2). What is the quotient? |
3x³ + 12x² + 26x + 61 + 132/x + 2 _3x³ + 2x + 5 3x³ + 12x² + 26x + 61 + 132/x – 2 3x⁴ + 2x² + 5x |

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? |
2x² + 5x – 18 |

Use synthetic division to solve (2x³ + 4x² – 35x + 15) / (x – 3). What is the quotient? |
2x² + 10x -5 |

Use synthetic division to solve (4x³ – 3x² + 5x + 6) / (x + 6). What is the quotient? |
4x² – 27x + 167 – 996/x – 6 4x² + 21x + 131 + 792/x + 6 4x² + 21x + 131 + 792/x – 6 _4x² – 27x + 167 – 996/x + 6 |

What divisor is represented by the synthetic division below? |
5 _x + 5 x – 5 |

The volume of a rectangular prism is (x3 – 3×2 + 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? |
x-3 + 7x-9/x²-2 |

If (x + 8) is a factor of f(x), which of the following must be true? |
f(-8) = 0 |

What dividend is represented by the synthetic division below? |
2x³ + 10x² + x + 5 |

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

If -1 is a root of f(x), which of the following must be true? |
A factor of f(x) is (x + 1). |

One root of f(x) = x³ – 9x² + 26x – 24 is x = 2. What are all the roots of the function? Use the Remainder Theorem. |
x = 2, x = 3, or x = 4 |

The area of a rectangle is 5x³ + 19x² + 6x – 18 with length x + 3. Using synthetic division, what is the width of the rectangle? |
5x² + 4x – 6 |

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

What is the completely factored form of f(x) = x3 – 2×2 – 5x + 6? |
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) |

According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3×5 – 2×4 + 9×3 – x2 + 12? |
f(x) = 3×5 – 2×4 – 9×3 + x2 – 12 |

According to the Rational Root Theorem, which could be a factor of the polynomial f(x) = 6×4 – 21×3 – 4×2 + 24x – 35? |
2x – 7 |

According to the Rational Root Theorem, the following are potential roots of f(x) = 2×2 + 2x – 24. |
_-4 and 3 -4, 2, and 3 -3 and 4 -3, 2, and 4 |

According to the Rational Root Theorem, which number is a potential root of f(x) = 9×8 + 9×6 – 12x + 7? |
7/3 |

The graph of f(x) = x6 – 2×4 – 5×2 + 6 is shown below. |
2 |

The polynomial function f(x) = 10×6 + 7x – 7 is graphed below. |
The root at point P may be 7/10. |

According to the Rational Roots Theorem, which statement about f(x) = 25×7 – x6 – 5×4 + x – 49 is true? |
Any rational root of f(x) is a factor of -49 divided by a factor of 25. |

According to the Rational Root Theorem, which statement about f(x) = 66×4 – 2×3 + 11×2 + 35 is true? |
Any rational root of f(x) is a factor of 35 divided by a factor of 66. |

Using the Rational Root Theorem, what are all the rational roots of the polynomial f(x) = 20×4 + x3 + 8×2 + x – 12? |
-4/5 and 3/4 |

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 9×4 – 2×2 – 3x + 4? |
±1/9, ±2/9, ±1/3, ±4/9, ±2/3, ±1, ±4/3, ±2, ±4 |

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 15×11 – 6×8 + x3 – 4x + 3? |
±1/15, ±1/5, ±1/3, ±3/5, ±1, ±3 |

According to the Rational Root Theorem, -7/8 is a potential rational root of which function? |
f(x) = 24×7 + 3×6 + 4×3 – x – 28 |

According to the Rational Root Theorem, the following are potential roots of f(x) = 60x² – 57x – 18. |
-1/4 |

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

What are the solutions of the equation x4 + 95×2 – 500 = 0? Use factoring to solve.▫️ |
x = ±√5 and x = ±10i |

Which equation is quadratic in form? |
_x6 + 6×4 + 8 = 0 7×6 + 36×3 + 5 = 0 4×9 + 20×3 + 25 = 0 |

Which quadratic equation is equivalent to (x2 – 1)2 – 11(x2 – 1) + 24 = 0? |
u2 – 11u + 24 = 0 where u = (x2 – 1) |

What are the solutions of the quadratic equation (x – 8)2 – 13(x – 8) + 30 = 0? Use u substitution to solve. |
x = -11 and x = -18 x = -2 and x = 5 x = 2 and x = -5 _x = 11 and x = 18 |

What are the solutions of the equation x4 + 3×2 + 2 = 0? Use u substitution to solve. |
x = ±i√2 and x = ±i |

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

What substitution should be used to rewrite 4×4 – 21×2 + 20 = 0 as a quadratic equation? |
u = x² |

Which equation is quadratic in form? |
_4(x – 2)2 + 3x – 2 + 1 = 0 8×5 + 4×3 + 1 = 0 10×8 + 7×4 + 1 = 0 9×16 + 6×4 + 1 = 0 |

What is the solution of the equation (x – 5)2 + 3(x – 5) + 9 = 0? Use u substitution and the quadratic formula to solve. |
x = -3±3i√3/2 _x = 7±3i√3/2 x = 2 x = 8 |

What are the solutions of the equation x6 – 9×3 + 8 = 0? Use u substitution to solve. |
x = 1 and x = 2 |

What are the solutions of the equation x4 – 5×2 – 14 = 0? Use factoring to solve. |
x = ± √7 and x = ± √2 x = ±i√7 and x = ±i√2 x = ±i√7 and x = ± √2 _x = ± √7 and x = ±i√2 |

What substitution should be used to rewrite 4×12 – 5×6 – 14 = 0 as a quadratic equation? |
u = x⁶ |

Which quadratic equation is equivalent to (x – 4)2 – (x – 4) – 6 = 0? |
u2 – u – 6 = 0 where u = (x – 4) |

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

What are the solutions of the equation x6 + 6×3 + 5 = 0? Use factoring to solve. |
x = -³√5 and x = -1 |

Let a and b be real numbers where a ≠ b ≠ 0. Which of the following functions could represent the graph below? |
f(x) = (x – a)²(x – b)⁴ |

Which statement describes the graph of f(x) = 4x⁷ + 40x⁶ + 100x⁵? |
The graph crosses the x axis at x = 0 and touches the x axis at x = -5. |

Which statement describes the graph of f(x) = -x4 + 3×3 + 10×2? |
The graph touches the x axis at x = 0 and crosses the x axis at x = 5 and x = -2. |

Which of the following graphs could be the graph of the function f(x) = -0.08x(x² – 11x + 18)? |
. . . . \ . .| . . . . . \. | . ./\ _________\|__/____\_ . . . . . . . |. . . . . .| . . . . . . . |. . . . . .| . . . . . . . |. . . . . .| |

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

What is the end behavior of the graph of the polynomial function f(x) = 3×6 + 30×5 + 75×4? |
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 → ∞. |

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

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

Which of the following graphs could be the graph of the function 0.03x²(x² – 25)? |
. . . .|. . . .|. . . .| . . . .|. . . .|. . . .| ______|_____|_____|______ . . . . .\__/|\__/ . . . . . . . . | . . . . . . . . | |

Which statement describes the graph of f(x) = -4x³ – 28x² – 32x + 64? |
The graph touches the x axis at x = -4 and crosses the x axis at x = 1. |

Which graph shows the end behavior of the graph of f(x) = 2x⁶ – 2x² – 5? |
. . . .|. . . . |. . . .| . . . . |. . . .|. . . | _______\__/|\__/_______ . . . . . . . . | . . . . . . . . | . . . . . . . . | |

Which graph has the same end behavior as the graph of f(x) = -3x³ – x² + 1? |
. .|. . . . . . .| . . | . . . . . | ____\______/|\___________ . . . .\__/. .|. .\ . . . . . . . . |. . .| . . . . . . . . |. . . | |

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

Which of the following graphs could be the graph of the function f(x) = x⁴ + x³ – x² – x? |
. . . . . . .|. |. . .| . . . . . . .| .|. . .| ___________-|___/________ . . . . . . . . |.- . . . . . . . . | |

# B- Polynomials

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