Remainder theorem/Factor theorem

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial p(x) by (x - c) is equal to p(c).

Front

What is the Factor Theorem?

Back

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

Front

How do you find the remainder when dividing a polynomial by a linear factor?

Back

To find the remainder, evaluate the polynomial at the value that makes the linear factor zero.

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

If p(x) = x^3 - 4, what is the remainder when divided by (x + 2)?

Back

The remainder is -12.

Front

If p(x) = x^3 - 5x^2 + 2x - 10, what is the remainder when divided by (x - 5)?

Back

The remainder is 0.

Front

Is (x - 7) a factor of (x^2 - 5x + 14)?

Back

No, (x - 7) 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 use synthetic division to evaluate f(5) for f(x) = 3x^2 - 9x - 20?

Back

Using synthetic division, f(5) = 10.

Front

What is the significance of the remainder in polynomial division?

Back

The remainder indicates how much is left over after division; if it is zero, the divisor is a factor.