Factor and Remainder Theorem

Front

What is the Factor Theorem?

Back

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

Front

What is the Remainder Theorem?

Back

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

Front

How do you evaluate a polynomial using synthetic division?

Back

To evaluate a polynomial f(x) at x = c using synthetic division, set up synthetic division with c and the coefficients of f(x), then compute the result.

Front

If f(x) = 3x^2 - 9x - 20, what is f(5)?

Back

f(5) = 10.

Front

When dividing p(x) = 9x^4 - 45x^3 + 37x^2 + x + 2 by (x - 2), what is p(2)?

Back

p(2) = -64.

Front

How can you determine if (x - 3) is a factor of 3x^3 + 10x^2 - x - 12?

Back

Evaluate f(3). If f(3) = 0, then (x - 3) is a factor. In this case, it is not a factor.

Front

What is the remainder when 2x^3 - 3x^2 + 4x - 5 is divided by (x - 1)?

Back

The remainder is -2.

Front

Which binomial is a factor of f(x) = x^3 - 6x^2 + 3x + 10?

Back

x + 1 is a factor.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor.

Front

What is the first step in synthetic division?

Back

Write down the coefficients of the polynomial and the value of c from (x - c).