divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder where p(x)=3x³+x²+2x+5 ,g(x)=1+2x+x²
Answers
Step-by-step explanation:
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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SIMILAR QUESTIONS
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Using division algorithm, find quotient and remainder dividing f(x) by g(x).
f(x)=3x
3
+x
2
+2x+5,g(x)=1+2x+x
2
Medium
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