What number should be subtracted from x³ - 4x² - 8x + 11 to make the number divisible by (x + 2)?

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Accepted Answer

To find the number to be subtracted from the polynomial P(x) = x³ - 4x² - 8x + 11 so that it becomes divisible by (x + 2), we use the Remainder Theorem. According to the theorem, the remainder when P(x) is divided by (x + 2) is P(-2).

Step 1: Calculate P(-2):
P(-2) = (-2)³ - 4(-2)² - 8(-2) + 11
= -8 - 4(4) + 16 + 11
= -8 - 16 + 16 + 11
= 3

Step 2: Since the remainder is 3, subtracting 3 from the polynomial will make it divisible by (x + 2).

Therefore, the number to be subtracted is 3.

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