.Divide 12 x³ -2x² +x +1 by 3x+1and write quotient and remainder.
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We know that the division algorithm states that:
Dividend=(Divisor×quotient)+Remainder
Here it is given that the dividend is p(x)=x
3
−3x
2
+x+2, the divisor is g(x), the quotient is x−2 and the remainder is −2x+4, therefore,
x
3
−3x
2
+x+2=[g(x)(x−2)]+(−2x+4)
⇒g(x)=
x−2
x
3
−3x
2
+x+2
The division is shown above.
Hence, from the above division, we get that the divisor is g(x)=x
2
−x+1
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