Remainder and Factor Theorems

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder of this division is f(c).

Front

What is the Factor Theorem?

Back

The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.

Front

How do you perform synthetic division?

Back

Synthetic division is a simplified form of polynomial long division. It involves using the coefficients of the polynomial and the root of the divisor to find the quotient and remainder.

Front

What is the result of (2x^3 + 5x^2 + 9) ÷ (x + 3)?

Back

2x^2 - x + 3.

Front

Which binomial is a factor of f(x) = x^3 + x^2 - 24x + 36?

Back

x + 6.

Front

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

Back

-113.

Front

What is the remainder when a^3 - 4 is divided by a + 2?

Back

-12.

Front

What is the purpose of the Remainder Theorem?

Back

To quickly find the remainder of a polynomial division without performing the full division.

Front

What does it mean if f(c) = 0 in the context of the Factor Theorem?

Back

It means that (x - c) is a factor of the polynomial f(x).

Front

What is the quotient of (2x^3 - 5x - 7) ÷ (x - 2) using synthetic division?

Back

2x^2 + 4x + 3 - 1/(x - 2).