Remainder Theorem

Front

What is the Remainder Theorem?

Back

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

Front

How do you find the remainder when dividing a polynomial by (x + 1)?

Back

To find the remainder, substitute -1 into the polynomial.

Front

Find the remainder when (3x^3 + 5x - 1) is divided by (x + 1).

Back

-9

Front

If (x^2 + 3x + 7) is divided by (x + 2), what is the remainder?

Back

5

Front

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

Back

Yes, because the remainder is 0 when divided.

Front

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

Back

No, because the remainder is not 0 when divided.

Front

What does it mean if the remainder is 0 when dividing a polynomial by (x - c)?

Back

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

Front

How can you use synthetic division to find the remainder?

Back

Use synthetic division with the root of the divisor (c) to find the remainder.

Front

What is synthetic division?

Back

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

Front

If f(x) = 2x^3 - 4x + 1, what is f(2)?

Back

f(2) = 2(2)^3 - 4(2) + 1 = 9.