PRE CALCULUS Pre-Calculus Polynomial Functions 4 — Questions and Answers
Question 1: What is the degree of the polynomial f(x) = (x² + 1)(x³ - 2x)(x - 4)?
- 5
- 6 (Correct answer)
- 7
- 4
Correct answer: 6
Multiplying the degrees: 2 + 3 + 1 = 6.
Question 2: Which polynomial has zeros at x = -2, x = 0, and x = 5 with all multiplicity 1?
- f(x) = x(x + 2)(x - 5) (Correct answer)
- f(x) = x(x - 2)(x + 5)
- f(x) = (x + 2)(x - 5)
- f(x) = x²(x - 2)(x + 5)
Correct answer: f(x) = x(x + 2)(x - 5)
Setting each factor to zero gives x = 0, x = -2, and x = 5.
Question 3: If a polynomial of degree 4 has exactly 2 distinct real zeros, what is the minimum number of complex zeros?
- 0
- 1
- 2 (Correct answer)
- 4
Correct answer: 2
A degree-4 polynomial must have 4 zeros (counting multiplicity); if 2 are real, at least 2 must be complex (in conjugate pairs).
Question 4: What is the leading term of f(x) = (3x² - 1)(2x³ + 4x)?
- 6x⁶
- 6x⁵ (Correct answer)
- 8x⁵
- -8x⁵
Correct answer: 6x⁵
Multiplying the leading terms: 3x² · 2x³ = 6x⁵.
Question 5: The graph of a polynomial function never has which of the following?
- Turning points
- x-intercepts
- Vertical asymptotes (Correct answer)
- A y-intercept
Correct answer: Vertical asymptotes
Polynomial functions are defined for all real x and have no vertical asymptotes.
Question 6: Which polynomial function is written in standard form?
- f(x) = 5 - 3x + x²
- f(x) = x³ + 2x² - x + 4 (Correct answer)
- f(x) = (x - 1)(x + 2)
- f(x) = 7 + x⁴ - 2x
Correct answer: f(x) = x³ + 2x² - x + 4
Standard form lists terms in descending order of degree: x³ + 2x² - x + 4.
Question 7: If f(x) = x³ - 4x, which statement about f is true?
- f is an even function
- f is an odd function (Correct answer)
- f is neither even nor odd
- f has no real zeros
Correct answer: f is an odd function
f(-x) = -x³ + 4x = -(x³ - 4x) = -f(x), confirming f is odd.
PRE CALCULUS Pre-Calculus Polynomial Functions 4
What is the degree of the polynomial f(x) = (x² + 1)(x³ - 2x)(x - 4)?