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)?

a) 1, 3
b) 3, 1
c) 1, 2
d) 2, 1

Answer 1

To find the remainder when a polynomial is divided by a linear expression, use the Remainder Theorem. 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.

Step-by-step explanation:

To find the remainder when P(x) is divided by (x-1), we can use the Remainder Theorem. This theorem states that if a polynomial P(x) is divided by (x-a), the remainder is equal to P(a).

Applying this to the given polynomial P(x), we find that the remainder when P(x) is divided by (x-1) is P(1), which is 0.

Similarly, to find the remainder when P(x) is divided by (x+2), we find that the remainder is P(-2), which is 1. Therefore, the answer is option d) 2, 1.