Multiple Choice Questions

One root of mc020-1.jpg is x =What are all the roots of the function? Use the Remainder Theorem.
  • x = -10, x = -5, or x = 5
  • (x - 2)(x + 4)(x - 6)
  • x = 2, x = 3, or x = 4
  • x = -2, x = 1, or x = 2
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?
  • -4/5 and 3/4
  • 5x^2+4x-6
  • 1.45 million
  • -4 and 3
What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?
  • x - 1
  • 5 - 6i
  • f(x) = 3x2 - 15x + 12
  • 3x - 5
Which statement describes the graph of this polynomial function?mc012-1.jpg
  • -2, -4, -3 + 2i, -3 - 2i
  • -5, 3, -4 + i, -4 - i
  • The graph crosses the x axis at x = 0 and touches the x axis at x = 3.
  • f(x) = (x + 2i)(x + 3i)(x - 2i)(x - 3i)
Which of the following is the complete list of roots for the polynomial function mc025-1.jpg?
  • -2, -4, -3 + 2i, -3 - 2i
  • 3 with multiplicity 4 and -6 with multiplicity 2
  • f(x) = 3x2 - 15x + 12
  • f(x) = 3x3 - 6x2 - 15x + 30
Which polynomial function has x intercepts -1, 0, and 2 and passes through the point (1, -6)?
  • f(x) = 3x2 - 15x + 12
  • f(x) = 3x2 - 18x + 24
  • f(x) = 3x3 - 3x2 - 6x
  • f(x) = (x + 5)(x + 5)(x + 5)(x + 4)(x - 2)(x - 9)
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)
  • f(x) has two complex roots and one real root.
  • f(x) = 3x2 - 18x + 24
  • f(x) = 3x3 - 3x2 - 6x
What divisor is represented by the synthetic division below?
  • 5 roots
  • f(x) = 2x2 + 2x - 4
  • x + 5
  • f(2k) = 0
What remainder is represented by the synthetic division below?
  • (x + 1)(2x - 3)(3x - 5)
  • x - 1
  • 0
  • b
Using the Rational Root Theorem, what are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x - 12?
  • 5 roots
  • f(x) = x4 - 3x2 - 4
  • -5, 3, -4 + i, -4 - i
  • -4/5 and 3/4
If f(-2) = 0, what are all the factors of the function mc023-1.jpg? Use the Remainder Theorem.
  • x = -2, x = 1, or x = 2
  • f(x) = 3x3 - 3x2 - 6x
  • (x + 1)(2x - 3)(3x - 5)
  • (x + 10)(x - 2)(x - 6)
Which of the following is the complete list of roots for the polynomial function mc026-1.jpg?
  • f(x) = 3x2 - 15x + 12
  • f(x) = 3x3 - 6x2 - 15x + 30
  • -2, -4, -3 + 2i, -3 - 2i
  • -5, 3, -4 + i, -4 - i
If (x - 2k) is a factor of f(x), which of the following must be true?
  • 5 - 6i
  • f(2k) = 0
  • f(x) = 3x2 - 18x + 24
  • x^2+4x+3
What is the polynomial function of lowest degree with lead coefficient 1 and roots i, -2, and 2?
  • f(x) = x4 - 3x2 - 4
  • f(x) = 3x3 - 6x2 - 15x + 30
  • f(x) = 3x3 - 3x2 - 6x
  • f(x) = 3x2 - 15x + 12
Which of the following describes the roots of the polynomial function mc009-1.jpg?
  • 3 with multiplicity 4 and -6 with multiplicity 2
  • -2, -4, -3 + 2i, -3 - 2i
  • The graph crosses the x axis at x = 0 and touches the x axis at x = 3.
  • -5, 3, -4 + i, -4 - i
According to the Rational Roots Theorem, which statement about f(x) = 25x7 - x6 - 5x4 + x - 49 is true?
  • 3 roots
  • 5 roots
  • Any rational root of f(x) is a factor of -49 divided by a factor of 25.
  • 3x - 5
Use synthetic division to solve (x4 - 1) ÷ (x - 1). What is the quotient?
  • x^2+x+1+2/x-1
  • x^3+x^2+x+1
  • -4/5 and 3/4
  • x^2+4x+3
According to the Rational Root Theorem, which number is a potential root of f(x) = 9x8 + 9x6 - 12x + 7?
  • 7/3
  • b
  • -1/4
  • 3 roots
Use synthetic division to solve (x3 + 1) ÷ (x - 1). What is the quotient?
  • x^2+x+1+2/x-1
  • (x + 1)(2x - 3)(3x - 5)
  • -4/5 and 3/4
  • f(x) = x4 - 3x2 - 4
Patricia is studying a polynomial function f(x). Three given roots of f(x) are mc018-1.jpg, 3 + 4i, andPatricia concludes that f(x) must be a polynomial with degreeWhich statement is true?
  • Patricia is not correct because both 3 - 4i and mc018-4.jpg must be roots.
  • The graph crosses the x axis at x = 0 and touches the x axis at x = 3.
  • Any rational root of f(x) is a factor of -49 divided by a factor of 25.
  • The graph crosses the x axis at x = -2 and x = 1 and touches the x axis at x = 0.
One factor of mc017-1.jpg is (x - 2). What are all the roots of the function? Use the Remainder Theorem.
  • -2, -4, -3 + 2i, -3 - 2i
  • f(x) = 3x2 - 15x + 12
  • x = -10, x = -5, or x = 5
  • x = -2, x = 1, or x = 2
One root of mc019-1.jpg is x = -What are all the roots of the function? Use the Remainder Theorem.
  • x = 2, x = 3, or x = 4
  • x = -2, x = 1, or x = 2
  • (x - 2)(x + 4)(x - 6)
  • x = -10, x = -5, or x = 5
Which statement describes the graph of this polynomial function?mc013-1.jpg
  • The graph crosses the x axis at x = 0 and touches the x axis at x = 3.
  • The graph crosses the x axis at x = -2 and x = 1 and touches the x axis at x = 0.
  • 3 with multiplicity 4 and -6 with multiplicity 2
  • Any rational root of f(x) is a factor of -49 divided by a factor of 25.
Use synthetic division to solve mc005-1.jpg. What is the quotient?
  • d
  • -4 and 3
  • x^2+4x+3
  • x^2+x+1+2/x-1
Which polynomial function has a leading coefficient of 1 and roots 2i and 3i with multiplicity 1?
  • f(x) = 2x2 + 2x - 4
  • f(x) = (x + 2i)(x + 3i)(x - 2i)(x - 3i)
  • f(x) = 3x3 - 3x2 - 6x
  • f(x) = 3x3 - 6x2 - 15x + 30
What is the completely factored form of f(x) = 6x3 - 13x2 - 4x + 15?
  • (x + 1)(2x - 3)(3x - 5)
  • (x + 10)(x - 2)(x - 6)
  • f(x) = x4 - 3x2 - 4
  • f(x) = 3x3 - 6x2 - 15x + 30
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
  • Any rational root of f(x) is a factor of -49 divided by a factor of 25.
  • 3 roots
  • 5 roots
According to the Rational Root Theorem, which could be a factor of the polynomial f(x) = 3x3 - 5x2 - 12x + 20?
  • -1/4
  • 3x - 5
  • 3 roots
  • x - 1
How many x intercepts appear on the graph of this polynomial function? mc010-1.jpg
  • f(x) = 3x3 - 3x2 - 6x
  • x^2+x+1+2/x-1
  • 3 x intercepts
  • f(x) = 3x2 - 15x + 12
One root of mc024-1.jpg is x =What are all the factors of the function? Use the Remainder Theorem.
  • f(x) = 3x3 - 3x2 - 6x
  • f(x) has two complex roots and one real root.
  • x = -2, x = 1, or x = 2
  • (x - 2)(x + 4)(x - 6)
Use synthetic division to solve mc009-1.jpg. What is the quotient?
  • d
  • The root at point P may be 3/5
  • f(x) = 2x2 + 2x - 4
  • x^2+x+1+2/x-1
According to the Rational Root Theorem, the following are potential roots of f(x) = 2x2 + 2x - 24.-4, -3, 2, 3, 4Which are actual roots of f(x)?
  • -1/4
  • Any rational root of f(x) is a factor of -49 divided by a factor of 25.
  • -4 and 3
  • f(x) = 3x5 - 2x4 - 9x3 + x2 - 12
The volume of a rectangular prism is mc010-1.jpg with height x +Using synthetic division, what is the area of the base?
  • f(x) = (x - 7)(x - 5)(x - 5)(x + 2)
  • 2x^2+5x-18
  • x^2+4x+3
  • 5 - 6i
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
  • 3 roots
  • 3x - 5
  • -9i
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) = (x + 5)(x + 5)(x + 5)(x + 4)(x - 2)(x - 9)
  • (x - 2)(x + 4)(x - 6)
  • x = 2, x = 3, or x = 4
  • f(x) has two complex roots and one real root.
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) = 3x3 - 3x2 - 6x
  • -4 and 3
  • 3x - 5
  • f(x) = 3x5 - 2x4 - 9x3 + x2 - 12
0 h : 0 m : 1 s

Multiple Choice Questions
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