**What must be subtracted from x**^{3} + 2x^{2} - 3x + 5 to make it exactly divisible by (...

^{3}+ 2x

^{2}- 3x + 5 to make it exactly divisible by (...

### Question

What must be subtracted from x^{3}+ 2x

^{2}- 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)

If x

x

∴ To make the remainder zero, 15 must be subtracted from the given polynomial

∴ x = 2

Substituting x = 2 in the given polynomial, gives

(2)

^{3}+ 2(2)^{2}- 3(2) + 5 = 15If x

_{3}2x^{2}- 3x + 5 is divisible by (x - 2), it implies that whenx

^{3}+ 2x^{2}- 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)

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The remainder is the answer

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 = 15If x

_{3}2x^{2}- 3x + 5 is divisible by (x - 2), it implies that whenx

^{3}+ 2x^{2}- 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