Question

Divide the following by long division method :-

x³-4x²-3x+5 by x-3

Whoever gives me the explained answer, I will mark him/her the brainliest!!! ​

Answer 1

$\large\underline{\sf{Solution-}}$

Here,

$\rm :\longmapsto\:Dividend = {x}^{3} - {4x}^{2} - 3x + 5$

$\rm :\longmapsto\:Divisor = x - 3$

So,

Using Long Division,

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\: {x}^{2} - x - 6\:\:}}}\\ {\underline{\sf{x - 3}}}& {\sf{\: {x}^{3} - {4x}^{2} - 3x + 5 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: - {x}^{3} + 3 {x}^{2} \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:\:}} \\ {{\sf{}}}& {\sf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - {x}^{2} - 3x + 5 \:  \:  \:  \:   \:  \:  \:  \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: \: \: \: \: \: {x}^{2} - 3x \:  \:  \:  \:  \:  \: \:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \: \: \: \: \: \: \: \: \: \: \: \: - 6x + 5  \:\:}} \\{\sf{}}& \underline{\sf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:6x - 18\:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \:  \: \:  \:  \:  \:  \: \: \: \: \: \: \: \: \: - 13\:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

So, we have

$\rm :\longmapsto\:Quotient \: = {x}^{2} - x - 6$

$\rm :\longmapsto\:Remainder = - 13$

$\rm :\longmapsto\:Divisor = x - 3$

$\rm :\longmapsto\:Dividend = {x}^{3} - {4x}^{2} - 3x + 5$

Verification

Consider,

$\rm :\longmapsto\:Divisor \times Quotient + Remainder$

$\: \: \rm \: = \: \:(x - 3)( {x}^{2} - x - 6) - 13$

$\: \: \rm \: = \: \: {x}^{3} - {x}^{2} - 6x - 3 {x}^{2} + 3x + 18 - 13$

$\: \: \rm \: = \: \: {x}^{3} - 4{x}^{2} - 3x + 5$

$\: \: \rm \: = \: \:Dividend$

Hence, Verified