Use the graph of the polynomial shown below to determine the remainder when divided by the following. 1) (x+1) 2) (x+2) 3) (x-1)

Question

i couldn’t add the picture so here’s a link to it: https://drive.google.com/file/d/1qbWw_88iXQOM7VpcBbJju4FcH8NUmZNw/view?usp=drivesdk

Answer 1

Let P(x) be the polynomial in the picture.

From the picture we use the facts that

P(-2) = 0

P(-1) = 8

P(1) = 0

Question 1)

P(x) = (x+1)Q(x) + R(x)

for some polynomials Q(x) and R(x), where R(x) is of degree 0.

Substituting x = -1:

P(-1) = (-1+1)Q(-1) + R(-1)

8 = R(-1)

Since R(x) is a constant, it is the constant 8.

Question 2) and 3)

Remainder is 0, because both (x+2) and (x-1) are factors, because both -2 and 1 are roots.