#1
What is the degree of the polynomial f(x) = 3x^4 + 2x^3 - 5x + 1?
#2
Which of the following is a polynomial function?
f(x) = 1/x
f(x) = √x
f(x) = 3x^2 - 2x + 5
f(x) = |x|
#3
Which of the following graphs represents a polynomial function of degree 2?
A parabola opening downward
A straight line
A cubic curve
A parabola opening upward
#4
Which of the following expressions represents a monomial?
3x^2 + 2x + 5
4x^2 + 7x - 3
5x^3 + 2x^2 - 6x + 1
2x^4
#5
What is the product of (x - 3) and (x + 4)?
x^2 - 7x - 12
x^2 + 7x + 12
x^2 - x - 12
x^2 + x - 12
#6
Which property of addition of polynomials is illustrated by the expression (2x^3 + 5x^2) + (3x^3 - 2x^2)?
Associative Property
Commutative Property
Distributive Property
Identity Property
#7
What is the sum of (4x^2 - 3x + 1) and (2x^2 + 5x - 2)?
6x^2 + 2x - 1
6x^2 + 8x - 1
6x^2 + 2x + 3
6x^2 + 2x - 3
#8
What is the quotient when (2x^3 + 3x^2 - 5x + 4) is divided by (x - 2)?
2x^2 + 7x + 2
2x^2 + 7x - 8
2x^2 - x + 2
2x^2 - x - 8
#9
What is the leading coefficient of the polynomial g(x) = -2x^5 + 3x^3 - 4x^2 + 7?
#10
What is the degree of the zero polynomial?
0
1
Undefined
Depends on the context
#11
Which of the following statements about polynomial division is true?
The divisor cannot be a polynomial of degree 0.
The quotient can have a degree greater than the dividend.
The remainder must have a degree less than the divisor.
Polynomial division is only defined for monic polynomials.
#12
Which of the following is a characteristic of the leading term of a polynomial?
It is the term with the highest degree.
It is always positive.
It has the lowest coefficient.
It determines the y-intercept.
#13
Which of the following is the correct expanded form of (x + 2)(x^2 - 3x + 1)?
x^3 - x^2 - 5x + 2
x^3 - 3x^2 + x - 2
x^3 - x^2 - x + 2
x^3 - 2x^2 - 3x + 2
#14
What is the y-intercept of the polynomial function f(x) = 2x^3 - 3x^2 + 4x - 5?
#15
Which of the following statements about polynomial functions is true?
All polynomial functions are continuous everywhere.
Polynomial functions can have a vertical asymptote.
Polynomial functions can have a domain that is all real numbers.
All polynomial functions have a finite number of turning points.
#16
What is the quotient when (4x^3 - 6x^2 + 8x - 10) is divided by (x - 1)?
4x^2 - 2x + 8
4x^2 - 2x + 6
4x^2 - 2x + 10
4x^2 - 2x + 12
#17
What is the maximum number of turning points a polynomial of degree n can have?
#18
What is the sum of the roots of the polynomial f(x) = x^2 - 6x + 9?
#19
Which of the following is a factor of the polynomial f(x) = x^3 - 5x^2 + 6x - 30?
(x - 5)
(x - 2)
(x + 5)
(x + 2)
#20
Which of the following is the correct factorization of the polynomial f(x) = x^4 - 16?
(x - 4)(x + 4)
(x - 2)(x + 2)(x^2 + 4)
(x - 4)(x + 4)(x^2 - 4)
(x - 8)(x + 8)
#21
If f(x) = 2x^3 - 5x^2 + 3x - 1, what are the zeros of the function?
1, 2
-1, 1/2
3, -1/2
1, -1/2
#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.
As x approaches positive infinity, g(x) approaches positive infinity, and as x approaches negative infinity, g(x) approaches negative infinity.
As x approaches positive infinity, g(x) approaches negative infinity, and as x approaches negative infinity, g(x) approaches negative infinity.
As x approaches positive infinity, g(x) approaches positive infinity, and as x approaches negative infinity, g(x) approaches positive infinity.
#23
Which theorem guarantees that a polynomial of degree n has exactly n roots?
Fundamental Theorem of Algebra
Intermediate Value Theorem
Rational Root Theorem
Factor Theorem
#24
Which of the following is the correct factorization of the polynomial f(x) = x^3 - 8?
(x - 2)(x + 2)(x^2 + 4)
(x - 2)(x + 2)(x - 4)
(x - 2)(x + 2)
(x - 8)(x + 8)
#25
Which of the following is true about the graph of a polynomial function with an odd degree?
It has an even number of turning points.
It crosses the x-axis an odd number of times.
It has only one real root.
It has a positive leading coefficient.