PRE CALCULUS Pre-Calculus Polynomial Functions 4

Question 1

What is the degree of the polynomial f(x) = (x² + 1)(x³ - 2x)(x - 4)?

Accepted Answer

6

Answer

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?

Accepted Answer

f(x) = x(x + 2)(x - 5)

Answer

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?

Accepted Answer

2

Answer

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)?

Accepted Answer

6x⁵

Answer

Multiplying the leading terms: 3x² · 2x³ = 6x⁵.

Question 5

The graph of a polynomial function never has which of the following?

Accepted Answer

Vertical asymptotes

Answer

Polynomial functions are defined for all real x and have no vertical asymptotes.

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