Factor Theorem-12

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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.

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