Question

Find the quotient and the remainder when f(x)=x³-3x²+5x-3 is divided by g(x)=x²-2​

Answer 1

Step-by-step explanation:

$\huge\underline{\overline{\mid{\bold{\purple{Given}}\mid}}}$

$\displaystyle \: \sf \: \longrightarrow \: f(x) = {x}^{3} - 3 {x}^{2} + 5x - 3 \\ \\ \displaystyle \: \sf \: \longrightarrow \: g(x) = {x}^{2} - 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

By dividing

$\displaystyle \: \sf \: \longrightarrow {x}^{2} - 2) {x}^{3} - 3 {x}^{2} + 5x - 3( x \\ \\ \displaystyle \: \sf \: \longrightarrow {x}^{2} ) - 3 {x}^{2} + 7x - 3(x \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \: \sf \: \longrightarrow {x}^{2} )7x - 9( x - 3 \: \: \: \: \: \: \: \: \: \:$

$\displaystyle \: \sf \: \longrightarrow quotient \: = \: x - 3 \: \: \: \\ \\ \displaystyle \: \sf \: \longrightarrow remainder \: = 7x - 9$