Polynomial Solutions Test

What divisor is represented by the synthetic division below?

x + 5

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

x - 1

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

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

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

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

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

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

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

x^2+4x+3

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

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

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

x^3+x^2+x+1

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

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

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

+-1/9,+-2/9,+-1/3,+-4/9,+-2/3,+-1,+-4/3,+-2,+-4

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

3x - 5

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

5 - 6i

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

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

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

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

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?

1.45 million

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

2x^2+5x-18

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

3

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

3 roots

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

The root at point P may be 3/5

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x3 - 7x + 11?

b

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?

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

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

d

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

d

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

f(2k) = 0

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

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

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?

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

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

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

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

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

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

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

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

-1/4

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

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

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

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

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

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

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

-5/2

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

-9i

What remainder is represented by the synthetic division below?

0

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

3 with multiplicity 4 and -6 with multiplicity 2

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

3 x intercepts

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)?

3, 4, 5, 6

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

5 roots

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

5x^2+4x-6

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

7/3

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?

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

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

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

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.

b

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

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

Which polynomial function could be represented by the graph below?

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

Which polynomial function could be represented by the graph below?

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

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

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

Which polynomial function could be represented by the graph below?

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

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

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

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

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

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

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

f(x) = x4 - 3x2 - 4

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.