Question

Divide 3x^3 + x^2 + 2x + 5 by 1 + 2x + x^2 and find the quotient and the remainder. Is 1 + 2x + x^2 a factor of 3x^3 + x^2 + 2x + 5

Answer 1

Answer:

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