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?
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?
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?
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)?
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)?
