Question

( 5x³-3x²) ÷ x² find quotient and remainder​

Answer 1

SOLUTION

TO DETERMINE

The quotient and remainder when

$\sf{(5 {x}^{3} - 3 {x}^{2} ) \div {x}^{2} }$

EVALUATION

Here the division is

$\sf{(5 {x}^{3} - 3 {x}^{2} ) \div {x}^{2} }$

So

Dividend = 5x³ - 3x²

Divisor = x²

Now

$\sf{(5 {x}^{3} - 3 {x}^{2} ) \div {x}^{2} }$

$\displaystyle \sf{ = \frac{5 {x}^{3} - 3 {x}^{2} }{ {x}^{2} } }$

$\displaystyle \sf{ = \frac{5 {x}^{3} }{ {x}^{2} } - \frac{3 {x}^{2} }{ {x}^{2} } }$

$\displaystyle \sf{ = 5 {x}^{3 - 2} - 3 {x}^{2 - 2} }$

$\displaystyle \sf{ = 5 {x}^{1} - 3 {x}^{0} }$

$\displaystyle \sf{ = 5x - 3}$

Hence

Quotient = 5x - 3

Remainder = 0

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Answer 2

$\underline{ \underline{ \sf\maltese \: Question}} :$

$\sf \red{find \: quotient \: and \: remainder \: of \: \: \frac{5 {x}^{3} - 3 {x}^{2} }{ {x}^{2} } }$

$\underline{ \underline{ \sf\maltese \: Answer}} :$

$\sf\Large\qquad\quad {5x-3} \\ \begin{array}{cc} \cline{2 - 2}\sf {x}^{2} )&\sf \ 5{x}^{3} - 3{x}^{2} \\&\sf - 5{x}^{3} \downarrow\\ \cline{2-2}& \sf \ \ \ \ -3{x}^{2} \\ &\sf \ - 3{x}^{2} \\ \cline{2-2} & \sf \ 0 \\ \cline{2-2} \end{array}\\\\\\ Divisor \rightarrow {x}^{2} \\ \\ Quotient \rightarrow {5x-3} \\\\Remainder \rightarrow 0$