# B: Polynomials

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question
What is the greatest common factor of the terms in the polynomial 3xÂ³ - 3xÂ² - 18x???(FPC)
3x
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What is the greatest common factor of the terms in the polynomial 8x? - 4xÂ³ - 18xÂ²?
2xÂ²
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Which product of prime polynomials is equivalent to 8x? + 36xÂ³ - 72xÂ²?
4xÂ²(2x - 3)(x + 6)
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What is the greatest common factor of the terms in the polynomial 12x? + 27xÂ³ + 6xÂ²?
3xÂ²
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5xÂ³ + 20xÂ² + 2x + 8 5xÂ²(x + 4) + 2(x + 4) Which is the completely factored form of his polynomial?
(5xÂ² + 2) (x + 4)
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Which product of prime polynomials is equivalent to 8xÂ³ - 2x?
2x(2x + 1)(2x - 1)
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7xÂ³ - 21xÂ² + 5x - 15 7xÂ²(x - 3) + 5(x -3) Which is the completely factored form of her polynomial?
(7xÂ² + 5) (x - 3)
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12x? + 30xÂ³ + 4xÂ² + 10x Ax(BxÂ² + 1) (2x + 5) B=[___________]
3
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Which is the completely factored form of 4xÂ³ + 10xÂ² - 6x?
2x(x + 3)(2x - 1)
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Which is the completely factored form of 12xÂ³ - 60xÂ² + 4x - 20?
4(3xÂ² + 1)(x - 5)
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Which product of prime polynomials is equivalent to 3x? - 81x?
3x(x - 3)(xÂ² + 3x + 9)
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What is the greatest common factor of the terms in the polynomial 4x? - 32xÂ³ - 60xÂ²?
4xÂ²
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3x? - 18xÂ³ + 9xÂ² -54x Ax(xÂ² + B) (x + C) C=[___________]
-6
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Which is the completely factored form of 3xÂ² - 12x - 15?
3(x + 1)(x - 5)
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What is the greatest common factor of the terms in the polynomial 12x? + 27xÂ³ + 6xÂ²?
3xÂ²
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Which polynomial is prime?
2x + 9
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4xÂ³ + 12xÂ² + 5x + 15 4xÂ²(x + 3) + 5(x + 3) Which is the completely factored form of her polynomial?
(4x2 + 5)(x + 3)
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Which polynomial is prime?
xÂ² + 6
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The long division below shows the first term of the quotient. Which polynomial should be subtracted from the dividend first? . . . .____xÂ²____ x+2|xÂ³+3xÂ²+x??(DoP)
xÂ³ + 2xÂ²
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What is the quotient (xÂ³ + 6xÂ² + 11x + 6) Ã· (xÂ² + 4x + 3)?
x + 2
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The quotient of (x? - 3xÂ³ - 3xÂ² - 10x + 15) and a polynomial is (xÂ² - 5). What is the polynomial?
xÂ³ + 2x - 3
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What is the quotient of the following division problem? . . . ._____x+2 x+1|xÂ²+3x+2 . . . .____xÂ²+x . . . .0+2x+2 . . . .___2x+2 . . . . . . . . 0
xÂ² + 3x + 2
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What is the remainder of the following division problem? . .___1 x|x+1 . .x___ . .0+1
1
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What is the first term of the quotient of the following division problem? (xÂ³ - 1) Ã· (x + 2)
xÂ²
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What is the quotient (xÂ³ + 8) Ã· (x + 2)?
xÂ² - 2x + 4
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What is the first step of the following division problem? (8xÂ³ - xÂ² + 6x + 7) Ã· (2x - 1)
Divide 8xÂ³ by 2x.
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What is the quotient of (xÂ³ + 3xÂ² - 4x - 12) / (xÂ² + 5x + 6)? [_________]
x - 2
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What is the quotient (xÂ³ - 3xÂ² + 5x - 3) Ã· (x - 1)?
xÂ² - 2x + 3
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If (x2 - 4) Ã· (x + 2) = x - 2, which polynomial should fill in the blank below? (x + 2) Â´ ______ = x2 - 4
x - 2
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What is the quotient (3x4 - 4x2 + 8x - 1) Ã· (x - 2)?
3xÂ³ + 6xÂ² + 8x + 24 + 47/x-2
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The quotient of (x? + 5xÂ³ - 3x - 15) and a polynomial is (xÂ³ - 3). What is the polynomial?
x + 5
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What is the quotient (125 - 8xÂ³) Ã· (25 + 10x + 4xÂ²)?
-2x + 5
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One factor of f(x) = 5xÂ³ + 5xÂ² - 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
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Use synthetic division to solve (xÂ³ + 1) Ã· (x - 1). What is the quotient?
xÂ³ - xÂ² + x
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One factor of f(x) = 4xÂ³ - 4xÂ² - 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
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One root of f(x) = xÂ³ - 4xÂ² - 20x + 48 is x = 6. What are all the factors of the function? Use the Remainder Theorem.
(x - 2)(x + 4)(x - 6)
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Use synthetic division to solve (3x? + 6xÂ³ + 2xÂ² + 9x + 10) / (x - 2). What is the quotient?
3xÂ³ + 12xÂ² + 26x + 61 + 132/x + 2 _3xÂ³ + 2x + 5 3xÂ³ + 12xÂ² + 26x + 61 + 132/x - 2 3x? + 2xÂ² + 5x
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The volume of a rectangular prism is 2xÂ³ + 9xÂ² - 8x - 36 with height x + 2. Using synthetic division, what is the area of the base?
2xÂ² + 5x - 18
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Use synthetic division to solve (2xÂ³ + 4xÂ² - 35x + 15) / (x - 3). What is the quotient?
2xÂ² + 10x -5
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Use synthetic division to solve (4xÂ³ - 3xÂ² + 5x + 6) / (x + 6). What is the quotient?
4xÂ² - 27x + 167 - 996/x - 6 4xÂ² + 21x + 131 + 792/x + 6 4xÂ² + 21x + 131 + 792/x - 6 _4xÂ² - 27x + 167 - 996/x + 6
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What divisor is represented by the synthetic division below? -5|2 10 1 5 . . |_-10 0-5 . . .2 .0 .1 0
5 _x + 5 x - 5
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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?
x-3 + 7x-9/xÂ²-2
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If (x + 8) is a factor of f(x), which of the following must be true?
f(-8) = 0
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What dividend is represented by the synthetic division below? -5|2 10 1 5 . . |_-10 0-5 . . .2 .0 .1 0
2xÂ³ + 10xÂ² + x + 5
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If f(1) = 0, what are all the roots of the function xÂ³ + 3xÂ² - x - 3? Use the Remainder Theorem.
x = -3, x = -1, or x = 1
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If -1 is a root of f(x), which of the following must be true?
A factor of f(x) is (x + 1).
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One root of f(x) = xÂ³ - 9xÂ² + 26x - 24 is x = 2. What are all the roots of the function? Use the Remainder Theorem.
x = 2, x = 3, or x = 4
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The area of a rectangle is 5xÂ³ + 19xÂ² + 6x - 18 with length x + 3. Using synthetic division, what is the width of the rectangle?
5xÂ² + 4x - 6
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According to the Rational Root Theorem, which statement about f(x) = 12xÂ³ - 5xÂ² + 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.
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What is the completely factored form of f(x) = x3 - 2x2 - 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)
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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?
f(x) = 3x5 - 2x4 - 9x3 + x2 - 12
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According to the Rational Root Theorem, which could be a factor of the polynomial f(x) = 6x4 - 21x3 - 4x2 + 24x - 35?
2x - 7
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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)?
_-4 and 3 -4, 2, and 3 -3 and 4 -3, 2, and 4
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According to the Rational Root Theorem, which number is a potential root of f(x) = 9x8 + 9x6 - 12x + 7?
7/3
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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)
2
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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?
The root at point P may be 7/10.
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According to the Rational Roots Theorem, which statement about f(x) = 25x7 - x6 - 5x4 + x - 49 is true?
Any rational root of f(x) is a factor of -49 divided by a factor of 25.
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According to the Rational Root Theorem, which statement about f(x) = 66x4 - 2x3 + 11x2 + 35 is true?
Any rational root of f(x) is a factor of 35 divided by a factor of 66.
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Using the Rational Root Theorem, what are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x - 12?
-4/5 and 3/4
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According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 9x4 - 2x2 - 3x + 4?
Â±1/9, Â±2/9, Â±1/3, Â±4/9, Â±2/3, Â±1, Â±4/3, Â±2, Â±4
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According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 15x11 - 6x8 + x3 - 4x + 3?
Â±1/15, Â±1/5, Â±1/3, Â±3/5, Â±1, Â±3
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According to the Rational Root Theorem, -7/8 is a potential rational root of which function?
f(x) = 24x7 + 3x6 + 4x3 - x - 28
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According to the Rational Root Theorem, the following are potential roots of f(x) = 60xÂ² - 57x - 18.
-1/4
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How many roots of f(x) are rational numbers? (Roots: 2, 3, 9/2)
3
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What are the solutions of the equation x4 + 95x2 - 500 = 0? Use factoring to solve.??
x = Â±?5 and x = Â±10i
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Which equation is quadratic in form?
_x6 + 6x4 + 8 = 0 7x6 + 36x3 + 5 = 0 4x9 + 20x3 + 25 = 0
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Which quadratic equation is equivalent to (x2 - 1)2 - 11(x2 - 1) + 24 = 0?
u2 - 11u + 24 = 0 where u = (x2 - 1)
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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
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What are the solutions of the equation x4 + 3x2 + 2 = 0? Use u substitution to solve.
x = Â±i?2 and x = Â±i
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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)
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What substitution should be used to rewrite 4x4 - 21x2 + 20 = 0 as a quadratic equation?
u = xÂ²
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Which equation is quadratic in form?
_4(x - 2)2 + 3x - 2 + 1 = 0 8x5 + 4x3 + 1 = 0 10x8 + 7x4 + 1 = 0 9x16 + 6x4 + 1 = 0
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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 = -3Â±3i?3/2 _x = 7Â±3i?3/2 x = 2 x = 8
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What are the solutions of the equation x6 - 9x3 + 8 = 0? Use u substitution to solve.
x = 1 and x = 2
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What are the solutions of the equation x4 - 5x2 - 14 = 0? Use factoring to solve.
x = Â± ?7 and x = Â± ?2 x = Â±i?7 and x = Â±i?2 x = Â±i?7 and x = Â± ?2 _x = Â± ?7 and x = Â±i?2
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What substitution should be used to rewrite 4x12 - 5x6 - 14 = 0 as a quadratic equation?
u = x?
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Which quadratic equation is equivalent to (x - 4)2 - (x - 4) - 6 = 0?
u2 - u - 6 = 0 where u = (x - 4)
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What substitution should be used to rewrite 6(x + 5)2 + 5(x + 5) - 4 = 0 as a quadratic equation?
u = (x + 5)
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What are the solutions of the equation x6 + 6x3 + 5 = 0? Use factoring to solve.
x = -Â³?5 and x = -1
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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)Â²(x - b)?
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Which statement describes the graph of f(x) = 4x? + 40x? + 100x??
The graph crosses the x axis at x = 0 and touches the x axis at x = -5.
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Which statement describes the graph of f(x) = -x4 + 3x3 + 10x2?
The graph touches the x axis at x = 0 and crosses the x axis at x = 5 and x = -2.
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Which of the following graphs could be the graph of the function f(x) = -0.08x(xÂ² - 11x + 18)?
. . . . . .| . . . . . . | . ./ _________|__/_____ . . . . . . . |. . . . . .| . . . . . . . |. . . . . .| . . . . . . . |. . . . . .|
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At which root does the graph of f(x) = (x - 5)Â³(x + 2)Â² touch the x axis?
-2
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What is the end behavior of the graph of the polynomial function f(x) = 3x6 + 30x5 + 75x4?
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 ? ?.
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At which root does the graph of f(x) = (x + 4)6(x + 7)5 cross the x axis?
-7
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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, ?).
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Which of the following graphs could be the graph of the function 0.03xÂ²(xÂ² - 25)?
. . . .|. . . .|. . . .| . . . .|. . . .|. . . .| ______|_____|_____|______ . . . . .__/|__/ . . . . . . . . | . . . . . . . . |
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Which statement describes the graph of f(x) = -4xÂ³ - 28xÂ² - 32x + 64?
The graph touches the x axis at x = -4 and crosses the x axis at x = 1.
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Which graph shows the end behavior of the graph of f(x) = 2x? - 2xÂ² - 5?