Question

Find x 10 2 by 5 x 8 4 by 5 divide 43 by 5 x

Answer 1

Hey mate I know the answer with 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+103x 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)=x2

−2x+3

This is the answer

Hope it helps .