This problem has two parts, Part A and Part B.

Question

Part A: Use the Remainder Theorem to find the remainder when p(x)=x^3+4x^2+5x+2 is divided by x+1.

Part B: Then, use the Factor Theorem to determine whether x+1 is a factor of p(x)=x^3+4x^2+5x+2.

Select one answer for Part A and one answer for Part B.

A. The remainder is 0
A. The remainder is 2
A. The remainder is 12
B. No, x + 1 is not a factor of p(x)
B. Yes, x + 1 is a factor of p (x)

can someone help me with this question I'm confused I feel like the remainder is 2 and x + 1 is a factor of p(x) am I wrong or could somebody please help

Answer 1

When p(x)=x^3+4x^2+5x+2 is divided by x+1
the p(-1) will be the remainder, so
p(-1) = (-1)^3 + 4(-1)^2 + 5(-1) + 2
= -1 + 4 - 5 + 2
= 0
Therefore x+1 is a factor of p(x)

Answer 2

Thank you for explaining properly this really helped!