Question

The polynomials P(x)=x^3−x−2 and Q(x)=x^2+2x+1 are multiplied and the result is completely simplified.

Which of these are terms in the resulting polynomial?

Choose all that are correct.
A. x3
B. 1
C. 2x^4
D. x^6
E. −5x

Answer 1

C. 2x^4; E. -5x

Explanation:

P(x) = x^3 − x − 2 and Q(x) = x^2 + 2x + 1

P(x) * Q(x) = (x^3 − x − 2)(x^2 + 2x + 1) =

= x^5 + 2x^4 + x^3 - x^3 - 2x^2 - x - 2x^2 - 4x - 2

= x^5 + 2x^4 - 4x^2 - 5x - 2

Answer: C. 2x^4; E. -5x