# Factor Theorem-4

### From Homeworkwiki

**The polynomials ax ^{3} + 3x^{2} - 13 and 2x^{3} -5x + a are divided by x + 2.**

**If the remainder is same in each case, find the value of a.**

**Solution:** Let f(x) =ax^{3} + 3x^{2} - 13 and g (x) = 2x^{3} -5x + a

The remainders when f (x) and g (x) are divided by x + 2 are f (-2) and g (-2)

f (-2) = a(-2)^{3} + 3(-2)^{2} - 13

= -8a + 12 - 13 = -8a - 1

g (-2) = 2.(-2)^{3} - 5(-2) + a = - 16 + 10 + a = -6 + a

Given, f (-2) = g (-2)

=> - 8a - 1 = - 6 + a

=> 6 - 1 = a + 8a

=> 5 = 9a

=> a = 5/9

Hence the value of a = 5/9