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 perform synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that uses the coefficients of the polynomial and the zero of the divisor.

Front

What is the first step in synthetic division?

Back

Write down the coefficients of the polynomial and the zero of the divisor.

Front

If f(x) = 2x^3 - 3x^2 + 4, what is f(2)?

Back

f(2) = 2(2)^3 - 3(2)^2 + 4 = 16 - 12 + 4 = 8.

Front

What does it mean if f(c) = 0?

Back

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

Front

What is the result of dividing 4x^2 - 24x + 35 by 2x - 5?

Back

The result is 2x - 7.

Front

Is (x - 3) a factor of x^3 - 3x^2 + 2x + 2?

Back

No, (x - 3) is not a factor.

Front

Is (x - 4) a factor of x^3 + x^2 - 16x - 16?

Back

Yes, (x - 4) is a factor.

Front

How do you determine if a polynomial has a factor?

Back

Evaluate the polynomial at the root of the factor; if the result is zero, it is a factor.