Factor Theorem-12
From Homeworkwiki
What numbers must be added to 3x3 + x2 - 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) = 3x3 + x2 - 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.
