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Standard VI
Mathematics
Question

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder.
p(x)=x3−3x2+5x−3
g(x)=x2−2
  1. q(x)=x−3,r(x)=7x+9
  2. q(x)=x+3,r(x)=−7x−9
  3. q(x)=x−3,r(x)=7x−9
  4. q(x)=x+3,r(x)=7x−9

A
q(x)=x+3,r(x)=−7x−9
B
q(x)=x−3,r(x)=7x+9
C
q(x)=x+3,r(x)=7x−9
D
q(x)=x−3,r(x)=7x−9
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Solution
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p(x)=x3−3x2+5x−3=x3−3x2−2x+6+7x−9
⇒p(x)=(x−3)(x2−2)+(7x−9)
g(x)=x2−2

Dividing p(x) by g(x), we get
Quotient q(x)=(x−3) and Remainder, R(x)=(7x−9)

Hence, option D.

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