find the quotient and remainder when the polynomial p(x)= x3 +x2-22x-5 divided by the polynomial g(x)= (x-5)
using division
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→ 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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