Multiple choice general knowledge

What number should be subtracted from x3 + 4x2 - 7x + 12 if it is to be perfectly divisible by x + 3?

  1. 42

  2. 39

  3. 13

  4. none
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A Correct answer
Explanation

Using the Remainder Theorem, for a polynomial P(x) to be divisible by (x + 3), P(-3) must be 0. P(-3) = (-3)^3 + 4(-3)^2 - 7(-3) + 12 = -27 + 36 + 21 + 12 = 42. Thus, 42 must be subtracted to make the remainder zero.

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