Question

Serena claims that (x+3) is a factor of p(x)=x4+6x3+12x2+10x+3. Which equation must Serena show to be true in order to prove her claim?

A
p(0)=3

B
p(3)=0

C
p(0)=−3

D
p(−3)=0

Answer 1

In order to prove that (x+3) is a factor of p(x), Serena must show that p(-3) = 0. This means that if we plug -3 into the polynomial p(x), the resulting value must be 0. Therefore, the correct answer is option D, p(-3)=0.

Explanation: