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 a linear factor?

Back

To find the remainder, substitute the value of c from (x - c) into the polynomial f(x) and calculate f(c).

Front

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

Back

The remainder is 5.

Front

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

Back

The remainder is -113.

Front

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

Back

The remainder is -64.

Front

What is the result of dividing (3x^3 + 5x - 1) by (x + 1)?

Back

The remainder is -9.

Front

Determine the remainder of (10x^4 - 50x^3 - 800) ÷ (x - 6).

Back

The remainder is 1,360.

Front

What does it mean if the remainder is 0 when dividing a polynomial by a linear factor?

Back

It means that the linear factor is a root of the polynomial.

Front

How can you verify the remainder using synthetic division?

Back

Perform synthetic division using the root of the linear factor and check the final value for 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.