Question

X^4+2x^3+3x^2+5x+3 ÷ x^2+3

Answer 1

Question:-

Find Quotient q(x) and Remainder r(x)?

Given:-

→p(x)=x⁴+2x³+3x²+5x+3

→g(x)=x²+3

$\rule{200}{1}$

To Find:-

→The Quotient and Remainder?[q(x)&r(x)]

$\rule{200}{1}$

Answer:-

๛Using Formula๛

→p(x)=q(x)×g(x)+r(x)

→$\frac{p(x)}{g(x)}$=q(x)+r(x)

๛Putting the Values๛

→$\frac{x^{4}+2x^{3}+3x^{2}+5x+3}{x^{2}+3}$=q(x)+r(x)

→$\frac{\cancel{x^{4}+2x^{3}+3x^{2}+5x+3}}{\cancel{x^{2}+3}}$=q(x)+r(x)

→$\frac{\cancel{x^{4}+2x^{3}+3x^{2}+5x+3}}{\cancel{x^{2}+3}}$=x²+2x+(-x+3)

๛q(x)=x²+2x

๛r(x)=(-x+3)

$\rule{200}{1}$

[Refer Attachment For Division]

$\rule{200}{2}$

Answer 2

$\tt{ \purple{ \implies{Quotient \: = {x}^{2} + 2x }}} \\ \\ \tt{ \purple{ \implies{remainder \: = 3 - x }}}$