# Factor Theorem-12

### From Homeworkwiki

**What numbers must be added to 3x ^{3} + x^{2} - 22x + 9, so that the result becomes exactly**

**divisible by x + 3.**

**Solution:** Let the number to be added be a. Then the expression becomes:

f(x) = 3x^{3} + x^{2} - 22x + 9 + a

For (x + 3) to be a factor of f(x), f( -3) = 0

f( -3) = 3.( -3)^{3} + ( -3)^{2} - 22( -3) + 9 + a

= -81 + 9 + 66 + 9 + a = 3 + a

Given that 3 + a = 0; => a = -3

Therefore, -3 should be added to the given expression to make the result exactly divisible by x + 3.