#1
What is the degree of the polynomial function f(x) = 3x^4 - 2x^3 + 5x^2 - 7x + 9?
4
ExplanationDegree is the highest power of the variable in the polynomial.
#2
Which of the following is a factor of the polynomial f(x) = x^3 - 4x^2 + x + 6?
x + 2
ExplanationA factor of a polynomial evenly divides the polynomial when substituted for the variable.
#3
Which of the following is a factor of the polynomial f(x) = x^4 - 6x^3 + 11x^2 - 6x + 1?
x - 1
ExplanationA factor of a polynomial evenly divides the polynomial when substituted for the variable.
#4
What are the roots of the equation 2x^2 - 5x - 3 = 0?
1, 3
ExplanationRoots are the solutions to the equation obtained by setting the polynomial equal to zero.
#5
Which of the following is NOT a polynomial function?
g(x) = √(x^2 + 1)
ExplanationA polynomial function is a function that can be expressed as a polynomial, and radical functions, like square roots, are not polynomials.
#6
What is the leading coefficient of the polynomial f(x) = 6x^4 - 3x^3 + 2x^2 - 5x + 7?
6
ExplanationThe leading coefficient is the coefficient of the term with the highest power of the variable.
#7
What is the degree of the polynomial function f(x) = 2x^6 + 5x^4 - x^3 + 3?
6
ExplanationDegree is the highest power of the variable in the polynomial.
#8
What is the sum of the roots of the equation x^2 - 5x + 6 = 0?
5
ExplanationThe sum of the roots of a quadratic equation equals the negation of the coefficient of x, divided by the leading coefficient.
#9
If f(x) = 2x^3 + 5x^2 - 4x + 7 and g(x) = x^2 - 3x + 2, what is f(x) / g(x)?
2x^2 - x + 3
ExplanationTo divide polynomials, perform polynomial long division or synthetic division.
#10
If f(x) = 3x^3 - 4x^2 + 2x - 5 and g(x) = x^2 + 2x + 3, what is f(x) * g(x)?
3x^5 - 4x^4 - 2x^3 - 16x^2 + 4x - 15
ExplanationTo multiply polynomials, distribute each term of one polynomial over the terms of the other polynomial.
#11
What is the quotient when the polynomial f(x) = 4x^3 - 9x^2 + 7x + 6 is divided by (x + 2)?
4x^2 - 17x + 34
ExplanationTo divide polynomials, perform polynomial long division or synthetic division.
#12
If f(x) = x^5 - 4x^4 + 6x^3 + 2x^2 - x + 9 and g(x) = x^3 - 2x^2 + 3x + 1, what is f(x) - g(x)?
x^5 - 4x^4 + 6x^3 - 3x^2 - 2x + 8
ExplanationTo subtract polynomials, subtract the corresponding terms.
#13
What is the quotient when the polynomial f(x) = 3x^4 - 5x^3 + 7x^2 - x + 2 is divided by (x - 1)?
3x^3 - 6x^2 + 7x - 1
ExplanationTo divide polynomials, perform polynomial long division or synthetic division.
#14
If f(x) = 2x^4 - 3x^3 + 4x^2 - 5x + 6 and g(x) = x^2 - 2x + 3, what is f(x) + g(x)?
2x^4 - 3x^3 + 6x^2 - 7x + 9
ExplanationTo add polynomials, add the corresponding terms.
#15
What is the remainder when the polynomial f(x) = 2x^4 - 5x^3 + 3x^2 + x - 9 is divided by (x - 3)?
18
ExplanationThe remainder theorem states that the remainder of a polynomial division is the value of the polynomial at the divisor.
#16
Which of the following is a root of the equation x^3 - 6x^2 + 11x - 6 = 0?
3
ExplanationA root of an equation satisfies the equation when substituted for the variable.
#17
What is the remainder when the polynomial f(x) = 2x^4 - 7x^3 + 3x^2 + 4x - 9 is divided by (x + 2)?
-19
ExplanationThe remainder theorem states that the remainder of a polynomial division is the value of the polynomial at the divisor.
#18
What is the remainder when the polynomial f(x) = x^5 - 3x^4 + 2x^3 + 5x^2 - x + 9 is divided by (x + 3)?
-65
ExplanationThe remainder theorem states that the remainder of a polynomial division is the value of the polynomial at the divisor.
#19
What is the remainder when the polynomial f(x) = 3x^5 - 7x^4 + 4x^3 + 2x^2 - 9x + 5 is divided by (x - 2)?
-11
ExplanationThe remainder theorem states that the remainder of a polynomial division is the value of the polynomial at the divisor.