Divide: 3x (5x² + 3x³+2) – (2x² + 8 - x) by (-2+3x).
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1
If we divide f(x)=3x
3
+x
2
+2x+5 by g(x) we get q(x)=(3x−5) as quotient and r(x)=(9x+10) as remainder.
By using division algorithm,
f(x)=g(x)q(x)+r(x)
⟹3x 3+x 2 +2x+5=g(x)(3x−5)+(9x+10)
⟹g(x)=
(3x−5)3x 3 +x 2 +2x+5−9x−10
⟹g(x)=
(3x−5)3x 3 +x 2−7x−5
Hence, g(x)=x 2+2x+1
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