Remainder Theorem

Front

What is the Remainder Theorem?

Back

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

Front

How do you find the remainder when dividing a polynomial by (x - c)?

Back

To find the remainder, substitute c into the polynomial p(x).

Front

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

Back

The remainder is 0.

Front

What is the remainder when (x^2 + 3x + 7) is divided by (x + 2)?

Back

The remainder is 5.

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

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

Back

No, (x - 7) is not a factor.

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

What is the significance of the Remainder Theorem in polynomial division?

Back

It simplifies the process of finding remainders without performing long division.

Front

How can you verify if (x - c) is a factor of a polynomial?

Back

If p(c) = 0, then (x - c) is a factor of the polynomial.