Question

P(x) is a polynomial. Here are a few values of P(x): P(-2)=1, P(-1)=3, P(1)=0, P(2)=4 What is the remainder when P(x) is divided by (x-1)? What is the remainder when P(x) is divided by (x+2)?

Answer 1

1

Explanation:

To find the remainder when a polynomial P(x) is divided by a linear factor (x - c), you can use the Remainder Theorem. The Remainder Theorem states that the remainder when P(x) is divided by (x - c) is equal to P(c).

For (x - 1):

P(1) = 0 (given)

For (x + 2):

P(-2) = 1 (given)

So, the remainder when P(x) is divided by (x - 1) is 0, and the remainder when P(x) is divided by (x + 2) is 1.