Question

Use the Remainder Theorem to find which of the following is a factor of 2x³ + 3x² – 5x – 6. 

x + 2

Answer 1

By remainder theorem we know that when a polynomial f (x) is divided by x – a, then the remainder is f(a).
Let f(x) = 2x³ + 3x² – 5x – 6 

`f(-2)=2(-2)^3(-2)^2-5(-2)-6`

=-16+12+10-6=0` 

Thus, (x + 2) is a factor of the polynomial f(x).