Question

What should be subtracted from 3x³ – 8x² + 4x – 3, so that the resulting expression has x + 2 as a factor? 

Answer 1

Let the required number be k.
Let f(x) = 3x³ – 8x² + 4x – 3 – k
According to the given information,
f (-2) = 0
3(-2)³ – 8(-2)² + 4(-2) – 3 – k = 0
-24 – 32 – 8 – 3 – k = 0
-67 – k = 0
k = -67
Thus, the required number is -67.