Question

P(x)⋅Q(x)=R(x); if P(x)=x+2 and R(x)=x3−2x2−6x+4, what is Q(x)?

Answer 1

Answer: Q(x) = x² - 4x + 2

Explanation:

P(x) · Q(x) = R(x) ⇒ Q(x) = R(x)/P(x)

R(x) = x³ - 2x² - 6x + 4 ÷ P(x) = x + 2

I will use synthetic division (but you can also use long division).

-2 | 1 -2 -6 4

| ↓ -2 8 -4

1 -4 2 0 ← remainder

The reduced polynomial is: x² - 4x + 2