Question

On dividing a polynomial 3x ^ 3 + 4x ^ 2 + 5x - 13 by a polynomial g(x) , the quotient x ^ 2 - 2x + 3and the remainder were (3x + 10) and (16x - 43) respectively. Find g(x) .


plz tell fast!!!​

Answer 1

Step-by-step explanation:

Given that,

let Polynomial p(x)=3x

3

+4x

2

+5x−13

quotient g(x)=3x+10

remainder r(x)=16x−43

g(x)=?

Now,

we know that

Euclid division lemma theorem,

p(x)=g(x)×q(x)+r(x)

3x

3

+4x

2

+5x−13=g(x)×(3x+10)+(16x−43)

3x

3

+4x

2

+5x−13−16x+43=g(x)×(3x+10)

3x

3

+4x

2

−11x+30=g(x)×(3x+10)

g(x)=

3x+10

3x

3

+4x

2

−11x+30

now, dividing,

3x+10)3x

3

+4x

2

−11x+30(x

2

−2x+3

−3x

3

+10x

2

_____________

−6x

2

−11x

−6x

2

−20x

_____________

9x+30

9x+30

____________

0

Hence, g(x)=x

2

−2x+3

This is the answer.