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Question

Question 4
On dividing x33x2+x+2 by a polynomial g(x), the quotient and remainder were x2 and 2x+4, respectively. Find g(x).

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Solution

Here in the given question,

Dividend =x33x2+x+2

Quotient =x2

Remainder =2x+4

Divisor = g(x)

We know that,

Dividend = Quotient × Divisor + Remainder

x33x2+x+2=(x2)×g(x)+(2x+4)x33x2+x+2(2x+4)=(x2)×g(x)
x33x2+3x2=(x2)×g(x)
g(x)=(x33x2+3x2)(x2)



g(x)=(x2x+1)


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