PRE CALCULUS Polynomials and Rational Functions

Question 1

What is the degree of the polynomial 3x⁴ - 2x² + x - 7?

Accepted Answer

4

Answer

The degree of a polynomial is the highest power of the variable. Here, the highest exponent is 4 (from the term 3x⁴).

Question 2

What is the Remainder Theorem?

Accepted Answer

When a polynomial f(x) is divided by (x - c), the remainder equals f(c)

Answer

The Remainder Theorem states that dividing f(x) by (x - c) gives a remainder equal to f(c). If f(c) = 0, then (x - c) is a factor.

Question 3

What is a vertical asymptote of a rational function?

Accepted Answer

A vertical line x = a where the function approaches infinity, occurring where the denominator equals zero

Answer

Vertical asymptotes occur at x-values where the denominator of a rational function equals zero (and the numerator does not), causing the function to approach infinity.

Question 4

How many roots can a polynomial of degree n have?

Accepted Answer

At most n real roots

Answer

The Fundamental Theorem of Algebra states a polynomial of degree n has exactly n roots (counting complex roots and multiplicity), but it has at most n real roots.

Question 5

What does the end behavior of a polynomial depend on?

Accepted Answer

The leading coefficient and the degree of the polynomial

Answer

End behavior (what happens as x → ±∞) is determined by the leading term. The degree determines the general shape, and the leading coefficient determines the direction.

PRE CALCULUS Practice Test

PRE CALCULUS Practice Test

PRE CALCULUS Polynomials and Rational Functions