What number should be subtracted from x3 − 4x2 − 8x + 11 to make the number divisible by (x+2)?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 3.
The given polynomial = x3 − 4x2 − 8x + 11
The Remainder Theorem states that if a polynomial f(x) is divided by (x - c), the remainder is f(c).
x + 2 = 0 ⇒ x = -2
Substituing x = -2 in the given equation,
(-2)3 − 4(-2)2 − 8(-2) + 11
= -8 - 16 + 16 + 11
= 3
Therefore, the required number is 3.