#1
What is the degree of the polynomial f(x) = 3x^4 + 2x^3 - 5x + 1?
4
ExplanationDegree corresponds to the highest power of the variable term.
#2
Which of the following is a polynomial function?
f(x) = 3x^2 - 2x + 5
ExplanationA polynomial function involves finite sums of powers of x.
#3
Which of the following graphs represents a polynomial function of degree 2?
A parabola opening upward
ExplanationDegree 2 polynomials have a characteristic parabolic shape.
#4
Which of the following expressions represents a monomial?
2x^4
ExplanationA monomial consists of one term.
#5
What is the product of (x - 3) and (x + 4)?
x^2 - 7x - 12
ExplanationUse the distributive property to multiply each term of one polynomial by each term of the other.
#6
Which property of addition of polynomials is illustrated by the expression (2x^3 + 5x^2) + (3x^3 - 2x^2)?
Commutative Property
ExplanationThe order of terms can be changed without altering the result.
#7
What is the sum of (4x^2 - 3x + 1) and (2x^2 + 5x - 2)?
6x^2 + 2x - 1
ExplanationAdd corresponding terms with the same power of x.
#8
What is the quotient when (2x^3 + 3x^2 - 5x + 4) is divided by (x - 2)?
2x^2 + 7x + 2
ExplanationDivide using polynomial long division or synthetic division.
#9
What is the leading coefficient of the polynomial g(x) = -2x^5 + 3x^3 - 4x^2 + 7?
-2
ExplanationLeading coefficient is the coefficient of the term with the highest degree.
#10
What is the degree of the zero polynomial?
Undefined
ExplanationThe zero polynomial has no terms, so its degree is undefined.
#11
Which of the following statements about polynomial division is true?
The divisor cannot be a polynomial of degree 0.
ExplanationDivision by a polynomial of degree 0 is not defined.
#12
Which of the following is a characteristic of the leading term of a polynomial?
It is the term with the highest degree.
ExplanationThe leading term determines the behavior of the polynomial.
#13
Which of the following is the correct expanded form of (x + 2)(x^2 - 3x + 1)?
x^3 - 2x^2 - 3x + 2
ExplanationExpand using distributive property.
#14
What is the y-intercept of the polynomial function f(x) = 2x^3 - 3x^2 + 4x - 5?
-5
ExplanationY-intercept is where the graph intersects the y-axis.
#15
Which of the following statements about polynomial functions is true?
Polynomial functions can have a domain that is all real numbers.
ExplanationPolynomials are defined for all real numbers.
#16
What is the quotient when (4x^3 - 6x^2 + 8x - 10) is divided by (x - 1)?
4x^2 - 2x + 8
ExplanationDivide using polynomial long division or synthetic division.
#17
What is the maximum number of turning points a polynomial of degree n can have?
n
ExplanationNumber of turning points equals degree minus one.
#18
What is the sum of the roots of the polynomial f(x) = x^2 - 6x + 9?
6
ExplanationSum of roots is the negative of the coefficient of the second-to-last term.
#19
Which of the following is a factor of the polynomial f(x) = x^3 - 5x^2 + 6x - 30?
(x - 5)
ExplanationA factor makes the polynomial equal zero for a specific value of x.
#20
Which of the following is the correct factorization of the polynomial f(x) = x^4 - 16?
(x - 2)(x + 2)(x^2 + 4)
ExplanationFactorization expresses a polynomial as a product of its factors.
#21
If f(x) = 2x^3 - 5x^2 + 3x - 1, what are the zeros of the function?
-1, 1/2
ExplanationZeros are the values of x where the function equals zero.
#22
What is the end behavior of the polynomial function g(x) = -2x^5 + 3x^3 - 4x^2 + 7?
As x approaches positive infinity, g(x) approaches negative infinity, and as x approaches negative infinity, g(x) approaches positive infinity.
ExplanationEnd behavior describes the function's behavior as x approaches positive or negative infinity.
#23
Which theorem guarantees that a polynomial of degree n has exactly n roots?
Fundamental Theorem of Algebra
ExplanationEvery polynomial equation has n solutions.
#24
Which of the following is the correct factorization of the polynomial f(x) = x^3 - 8?
(x - 2)(x + 2)(x^2 + 4)
ExplanationFactorization expresses a polynomial as a product of its factors.
#25
Which of the following is true about the graph of a polynomial function with an odd degree?
It crosses the x-axis an odd number of times.
ExplanationOdd-degree polynomials intersect the x-axis an odd number of times.