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Standard VIII
Mathematics
Question

On dividing x3−3x2+x+2 by a polynomial g(x), the quotient and remainder were x−2 and −2x+4, respectively. Find g(x).
  1. x2+x+1
  2. x2−x+1
  3. x2−x−1
  4. x2+1

A
x2+x+1
B
x2−x+1
C
x2−x−1
D
x2+1
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Solution
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Dividend =p(x)=x3−3x2+x+2
Quotient =q(x)=x−2
Remainder =r(x)=2x+4
By division algorithm, p(x)=q(x)g(x)+r(x)
⇒g(x)=p(x)−r(x)q(x)
⇒g(x)=x3−3x2+x+2+2x−4x−2
⇒g(x)=x3−3x2+3x−2x−2
So, g(x)=x2−x+1

295375_313210_ans_c7bf1dbe35284abf9bbaf59a4cc91648.png

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