Practice Remainder and Factor Theorems

Front

What does the degree of a polynomial determine?

Back

The maximum number of x-intercepts.

Front

What does (x – r) being a factor of P(x) imply?

Back

P(r) = 0.

Front

What is the remainder of (3x^3 - 5x^2 - 4x + 1) ÷ (x + 3)?

Back

-113.

Front

How should the answer for the polynomial division be written?

Back

2x^3 - x^2 - 25x - 12.

Front

What is the degree of the polynomial f(x) = x^3(x + 3)^2(x - 5)?

Back

Degree: 6.

Front

Define the Remainder Theorem.

Back

The Remainder Theorem states that the remainder of the division of a polynomial P(x) by (x - r) is P(r).

Front

What is the Factor Theorem?

Back

The Factor Theorem states that (x - r) is a factor of P(x) if and only if P(r) = 0.

Front

How can you find the maximum number of x-intercepts of a polynomial?

Back

By determining the degree of the polynomial.

Front

What is the relationship between the degree of a polynomial and its turning points?

Back

A polynomial of degree n can have at most n - 1 turning points.

Front

What does it mean if P(r) ≠ 0 for a polynomial P(x)?

Back

It means that (x - r) is not a factor of P(x).