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Question

On dividing the polynomial p(x)=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

We know that the division algorithm states that:
Dividend=(Divisor×quotient)+Remainder

Here it is given that the dividend is p(x)=x33x2+x+2, the divisor is g(x), the quotient is x2 and the remainder is 2x+4, therefore,

x33x2+x+2=[g(x)(x2)]+(2x+4)g(x)=x33x2+x+2x2

The division is shown above.

Hence, from the above division, we get that the divisor is g(x)=x2x+1


634261_562443_ans_0c222cee54e34e3dbc58069ee07d600a.png

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