Question

Use remainder theorem for x^3+8x^2+11x-20 by x-5.

Answer 1

The remainder theorem:

When a polynomial p(x) is divided by a linear polynomial (x - a), then the remainder is equal to p(a).

To find the remainder we need:

1. Find the zero of the linear polynomial.
2. Substitute it in the given polynomial.

As result we get the remainder.

1. Step:

x - 5 = 0 ⇔ x = 5

2. Step:

Substitute 5 to x³ + 8x² + 11x - 20:

5³ + 8×5² + 11×5 - 20 = 125 + 8×25 + 55 - 20 = 160 + 200 = 360

So:

The remainder is 360.