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

Step-by-step 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