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What must be subtracted from x3 + 2x2 - 3x + 5 to make it exactly divisible by (...


Question

What must be subtracted from x3 + 2x2 - 3x + 5 to make it exactly divisible by (x - 2)?

Options

A) 17

B) 15

C) 12

D) 9

The correct answer is B.

Explanation:

Equating the divisor to zero, gives (x - 2) = 0
∴ x = 2
Substituting x = 2 in the given polynomial, gives
(2)3 + 2(2)2 - 3(2) + 5 = 15
If x3 2x2 - 3x + 5 is divisible by (x - 2), it implies that when
x3 + 2x2 - 3x + 5 is divided by (x - 2), it will leave a remainder of zero
∴ To make the remainder zero, 15 must be subtracted from the given polynomial

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Discussion (2)

  • The remainder is the answer

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  • Equating the divisor to zero, gives (x - 2) = 0
    ∴ x = 2
    Substituting x = 2 in the given polynomial, gives
    (2)3 + 2(2)2 - 3(2) + 5 = 15
    If x3 2x2 - 3x + 5 is divisible by (x - 2), it implies that when
    x3 + 2x2 - 3x + 5 is divided by (x - 2), it will leave a remainder of zero
    ∴ To make the remainder zero, 15 must be subtracted from the given polynomial

    Reply
    Like