Question

dividing 3x² + 4x + 5 x 0 - 13 by
the quotient and remainder
polynomial g(x)​

Answer 1

Answer:

$\Large\underline{\underline{\sf{ \color{magenta}{\qquad Given \qquad} }}}$

Given that,

let Polynomial p(x)=3x 3 +4x² +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)

p(x)=g(x) × q(x) + r(x)3x 3 +4x² + 5x − 13 = g(x) × (3x+10) + (16x−43)

3x3 +4x² + 5x−13 − 16x+43=g(x) × (3x+10)

$g(x) = \frac{3x³+ 4x² - 11x + 30}{3x + 10}$

now, dividing,

3x+10)3x³ +4x² −11x + 30(x² −2x+3−3x

3 + 10x²

_____________

−6x² −11x

−11x−6x² −20x

_____________

9x+30

9x+309x+30

_____________

0

0Hence, g(x)=x² −2x + 3

This is the answer.

Answer 2

Given that,

let Polynomial p(x)=3x 3 +4x² +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)

p(x)=g(x) × q(x) + r(x)3x 3 +4x² + 5x − 13 = g(x) × (3x+10) + (16x−43)

3x3 +4x² + 5x−13 − 16x+43=g(x) × (3x+10)

g(x) = \frac{3x³+ 4x² - 11x + 30}{3x + 10}g(x)=

3x+10

3x³+4x²−11x+30

now, dividing,

3x+10)3x³ +4x² −11x + 30(x² −2x+3−3x

3 + 10x²

_____________

−6x² −11x

−11x−6x² −20x

_____________

9x+30

9x+309x+30

_____________

0

0Hence, g(x)=x² −2x + 3

This is the answer.