Question

What number should be added to x^3-9x-2x+3 so that the reminder may be 5 when divided by (x-2)

Answer 1

SOLUTION

TO DETERMINE

The number should be added to x³ - 9x² -2x + 3 so that the reminder may be 5 when divided by (x-2)

EVALUATION

Let k be the required number should be added to x³ - 9x² -2x + 3 so that the reminder may be 5 when divided by (x-2)

Let

$\sf{f(x) = {x}^{3} - 9 {x}^{2} - 2x + 3 + k }$

$\sf{g(x) = x - 2}$

For Zero of the polynomial g(x) we have

g(x) = 0

$\implies \sf{x - 2 = 0}$

$\implies \sf{x = 2 }$

So by the Remainder Theorem the required Remainder when f(x) is divided by g(x) is

f(2)

$\sf{ = {(2)}^{3} - 9 \times {(2)}^{2} - 2 \times 2 + 3 + k }$

$\sf{ = 8 - 36 - 4 + 3 + k}$

$\sf{ = k - 29}$

According to the question

$\sf{ k - 29 = 5}$

$\sf{ \implies \: k = 34}$

FINAL ANSWER

Hence the required number = 34

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