Question

If a polynomial p(x)=x³-3x²+5x-3 is divided by polynomial g(x)=x²-2,the quotient and remainder are:​

Answer 1

$\rule{200}3$

Question :-

If a polynomial p(x)=x³-3x²+5x-3 is divided by polynomial g(x)=x²-2,the quotient and remainder are:

$\rule{200}3$

Given :-

• p(x)=x³ - 3x² + 5x - 3

• g(x)=x² - 2

$\rule{200}3$

To find :-

• Quotient and remainder

$\rule{200}3$

Solution :-

$\boxed{\begin{array}{l | n | r}\sf x^2-2&\sf x^3-3x^2+5x-3&\sf x-3\\ &\sf x^3\:\:\:\: \:\:\:\:\: \:\:\:-2x\\ & ( - )\:\:\:\:\:\:\:\: \:\:\:\:( + )\\&\rule{80}{0.8}\\&\sf\qquad -3x^2+7x-3\\ &\sf\qquad-3x^2\:\:\:\:\:\: \:\:\:\:+6\\ &\qquad( + )\:\:\:\:\:\:\:\: \:\:\:\:( - )\\&\quad\rule{80}{0.8}\\&\qquad\qquad\sf 7x-9\end{array}}$

• Quotient = x - 3

• Remainder = 7x - 9

$\rule{200}3$

Answer 2

$\huge\sf\pink{Answer}$

☞ Quotient = x-3

☞ Remainder = 7x-9

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ p(x) = x³-3x²+5x-3 is divided by g(x) = x²-2

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

◈ The Quotient And the Remainder?

$\rule{110}1$

$\huge\sf\purple{Steps}$

So here is your Division,

$\sf \green{{x}^{2} - 2 }){{x}^{3} - 3 {x}^{2} + 5x - 3}{(}\red{x - 3} \\ \sf \qquad \: \: \: \: \: {x}^{3} \qquad \: \: \: \: \: - 2x \\ \sf \qquad \: \: \: \ ( - ) \qquad \: \: ( + ) \\ \underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf \qquad \: \: \: \: \: \: \: \: \: \: \: - 3 {x}^{2} + 7x - 3 \\ \sf \qquad \: \: \: \: \: \: \: \: \: \: \:- 3 {x}^{2} \qquad \: \: + 6 \\ \sf \qquad \: \: \: \: \: \: \: \: \: \: ( + ) \qquad \: \: ( - ) \\ \underline{ \qquad \qquad \qquad \qquad \qquad \qquad \: } \\ \sf \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \orange{7x - 9}\\ \underline{ \qquad\qquad\qquad\qquad\qquad\qquad \:}$

$\rule{170}3$