Question

1. Using division algorithm, divide the polynomial
f(x) by the polynomial g(x) and find quotient
and remainder.
(1) f(x) 3 x cube + x square + 2 X + 5 and the GX is 1+ 2x 1 +x square
​

Answer 1

Step-by-step explanation:

If we divide f(x)=3x3 +x2+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 3+x 2 +2x+5−9x−10/(3x-5)

⟹g(x)= 3x3+x2 −7x−5/(3x-5)

Hence, g(x)=x2+2x+1

√\______anushka♥