question

The volume of a rectangular prism is mc010-1.jpg with height x + 2. Using synthetic division, what is the area of the base?

answer

2x^2+5x-18

question

The area of a rectangle is mc011-1.jpg with length x + 3. Using synthetic division, what is the width of the rectangle?

answer

5x^2+4x-6

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

What divisor is represented by the synthetic division below?

answer

x + 5

question

One factor of mc017-1.jpg is (x - 2). What are all the roots of the function? Use the Remainder Theorem.

answer

x = -2, x = 1, or x = 2

question

Use synthetic division to solve (x4 - 1) รท (x - 1). What is the quotient?

answer

x^3+x^2+x+1

question

If f(-5) = 0, what are all the factors of the function mc022-1.jpg? Use the Remainder Theorem.

answer

(x - 2)(x + 5)(x - 3)

question

The price that a company charged for a computer accessory is given by the equation 100-10x^2 where x is the number of accessories that are produced, in millions. It costs the company $10 to make each accessory. The company currently produces 2 million accessories and makes a profit of 100 million dollars. What other number of accessories produced yields approximately the same profit?

answer

1.45 million

question

One root of mc024-1.jpg is x = 6. What are all the factors of the function? Use the Remainder Theorem.

answer

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

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 mc019-1.jpg is x = -10. What are all the roots of the function? Use the Remainder Theorem.

answer

x = -10, x = -5, or x = 5

question

Use synthetic division to solve mc005-1.jpg. What is the quotient?

answer

x^2+4x+3

question

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

answer

7/3

question

According to the Rational Root Theorem, the following are potential roots of f(x) = 60x2 - 57x - 18.
mc015-1.jpg, mc015-2.jpg, 3, 6

answer

-1/4

question

According to the Rational Root Theorem, which could be a factor of the polynomial f(x) = 3x3 - 5x2 - 12x + 20?

answer

3x - 5

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, 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

question

The polynomial function f(x) = 5x5 + 3x - 3 is graphed below.

answer

The root at point P may be 3/5

question

The polynomial function f(x) = 3x5 - 2x2 + 7x models the motion of a roller coaster. The roots of the function represent when the roller coaster is at ground level. Which answer choice represents all potential values of when the roller coaster is at ground level? Begin by factoring x to create a constant term.

answer

b

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) = 5x3 - 7x + 11?

answer

b

question

The graph of f(x) = 2x3 - 19x2 + 57x - 54 is shown below.

answer

3

question

According to the Rational Root Theorem, the following are potential roots of f(x) = 6x4 + 5x3 - 33x2 - 12x + 20.
mc014-1.jpg, -2, 1, mc014-2.jpg

answer

-5/2

question

One root of a third degree polynomial function f(x) is -5 + 2i. Which statement describes the number and nature of all roots for this function?

answer

f(x) has two complex roots and one real root.

question

Which of the following is the complete list of roots for the polynomial function mc026-1.jpg?

answer

-5, 3, -4 + i, -4 - i

question

If 5 + 6i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?

answer

5 - 6i

question

Which statement describes the graph of this polynomial function?
mc012-1.jpg

answer

The graph crosses the x axis at x = 0 and touches the x axis at x = 3.

question

If 9i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?

answer

-9i

question

One root of a third degree polynomial function f(x) is -5 + 2i. Which statement describes the number and nature of all roots for this function?

answer

f(x) has two complex roots and one real root.

question

Which of the following describes the roots of the polynomial function mc009-1.jpg?

answer

3 with multiplicity 4 and -6 with multiplicity 2

question

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?
f(x) = 4x5 - 3x

answer

5 roots

question

Which statement describes the graph of this polynomial function?
mc013-1.jpg

answer

The graph crosses the x axis at x = -2 and x = 1 and touches the x axis at x = 0.

question

If 9i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?

answer

-9i

question

The polynomial function f(x) is a fourth degree polynomial. Which of the following could be the complete list of the roots of f(x)?

answer

3, 4, 5, 6

question

Which statement describes the graph of this polynomial function?
mc012-1.jpg

answer

The graph crosses the x axis at x = 0 and touches the x axis at x = 3.

question

According to the Fundamental Theorem of Algebra, which polynomial function has exactly 6 roots?

answer

d

question

How many x intercepts appear on the graph of this polynomial function?
mc010-1.jpg

answer

3 x intercepts

question

Which polynomial function has x intercepts -1, 0, and 2 and passes through the point (1, -6)?

answer

f(x) = 3x3 - 3x2 - 6x

question

Which second degree polynomial function f(x) has a lead coefficient of 3 and roots 4 and 1?

answer

f(x) = 3x2 - 15x + 12

question

Which polynomial function f(x) has a leading coefficient of 1, roots -4, 2, and 9 with multiplicity 1, and root -5 with multiplicity 3?

answer

f(x) = (x + 5)(x + 5)(x + 5)(x + 4)(x - 2)(x - 9)

question

Which polynomial function could be represented by the graph below?

answer

f(x) = 3x2 - 18x + 24

question

Which polynomial function has a leading coefficient of 1 and roots 2i and 3i with multiplicity 1?

answer

f(x) = (x + 2i)(x + 3i)(x - 2i)(x - 3i)

question

Which is the polynomial function of lowest degree with lead coefficient of 3 and roots mc025-1.jpg and 2?

answer

f(x) = 3x3 - 6x2 - 15x + 30

question

Which polynomial function could be represented by the graph below?

answer

f(x) = 2x2 + 2x - 4

question

Which polynomial function could be represented by the graph below?

answer

f(x) = 3x2 - 18x + 24

question

Which polynomial function has a leading coefficient of 1, roots -2 and 7 with multiplicity 1, and root 5 with multiplicity 2?

answer

f(x) = (x - 7)(x - 5)(x - 5)(x + 2)

question

Which polynomial function could be represented by the graph below?

answer

f(x) = -2x3 - 2x2 + 12x

question

Which polynomial function has x intercepts -1, 0, and 2 and passes through the point (1, -6)?

answer

f(x) = 3x3 - 3x2 - 6x

question

Which second degree polynomial function f(x) has a lead coefficient of 3 and roots 4 and 1?

answer

f(x) = 3x2 - 15x + 12

question

What is the polynomial function of lowest degree with lead coefficient 1 and roots i, -2, and 2?

answer

f(x) = x4 - 3x2 - 4

question

One root of mc020-1.jpg is x = 2. What are all the roots of the function? Use the Remainder Theorem.

answer

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

question

Patricia is studying a polynomial function f(x). Three given roots of f(x) are mc018-1.jpg, 3 + 4i, and 10. Patricia concludes that f(x) must be a polynomial with degree 4. Which statement is true?

answer

Patricia is not correct because both 3 - 4i and mc018-4.jpg must be roots.

question

Which of the following is the complete list of roots for the polynomial function mc025-1.jpg?

answer

-2, -4, -3 + 2i, -3 - 2i

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 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

What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?

answer

x - 1

question

What is the completely factored form of f(x) = 6x3 - 13x2 - 4x + 15?

answer

(x + 1)(2x - 3)(3x - 5)

question

If (x - 2k) is a factor of f(x), which of the following must be true?

answer

f(2k) = 0

question

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?
(9x + 7)(4x + 1)(3x + 4) = 0

answer

3 roots

question

Which polynomial function f(x) has a leading coefficient of 1, roots -4, 2, and 9 with multiplicity 1, and root -5 with multiplicity 3?

answer

f(x) = (x + 5)(x + 5)(x + 5)(x + 4)(x - 2)(x - 9)

question

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

answer

x^2+x+1+2/x-1

question

Use synthetic division to solve mc009-1.jpg. What is the quotient?

answer

d

question

If f(-2) = 0, what are all the factors of the function mc023-1.jpg? Use the Remainder Theorem.

answer

(x + 10)(x - 2)(x - 6)