# Factor Theorem-3

### From Homeworkwiki

**If the polynomial f (x) = 2x ^{3} -ax^{2} + 4x - 1 leaves a remainder - 37 when divided by x + 2,**

**find the value of a.**

**Solution:** By remainder theorem, when f(x) is divided by x + 2, the remainder = f (-2)

f (-2) = 2 (-2)^{3} - a(-2)^{2} + 4(-2) - 1

= - 16 - 4a - 8 - 1

= - 25 - 4a

Given Remainder = - 37

=> - 25 - 4a = - 37

=> 4a = 37 - 25 = 12

=> a = 12 / 4 = 3