Question

5 by
11. On dividing 3r' + r + 2
remainder are (3.x - 5) and (9x + 10) respectively. Find g(x).
2. Verify division algorithm for the polynomials f(x) = 8 + 20x+7-6x?
and g(x) = 2 + 5x - 3r.
ཀརལ – 11r – 12.​

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