Question

$(m ^{2} - 5m + 6)by(m - 3)$
divide:​

Answer 1

Answer:

-m+2

m^2 -5m+6 divide = -m+2

Answer 2

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

Given expression is

$\rm :\longmapsto\:\dfrac{ {m}^{2} - 5m + 6 }{m - 3}$

Now, let split the middle term in numerator.

We have to split the middle term in such a way that on multiplication we get 6 and on addition we get - 5. So, such pair is - 2 and -3.

So, given expression

$\rm :\longmapsto\:\dfrac{ {m}^{2} - 5m + 6 }{m - 3}$

can be split as

$\rm \:  =  \:  \: \:\dfrac{ {m}^{2} - 2m - 3m + 6 }{m - 3}$

$\rm \:  =  \:  \: \:\dfrac{ m(m - 2) - 3(m - 2) }{m - 3}$

$\rm \:  =  \:  \: \:\dfrac{ (m - 2) (m - 3) }{m - 3}$

$\rm \:  =  \:  \: m - 2$

Hence,

$\rm :\longmapsto\:\dfrac{ {m}^{2} - 5m + 6 }{m - 3} = m - 2$

Alternative Method :-

Given expression is

$\rm :\longmapsto\:\dfrac{ {m}^{2} - 5m + 6 }{m - 3}$

Using Long Division, we have

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\: m - 2\:\:}}}\\ {\underline{\sf{m - 3}}}& {\sf{\: {m}^{2} - 5m + 6 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \:  \:  \: \: \:  -  {m}^{2} + 3 m   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:\:}} \\ {{\sf{}}}& {\sf{\: \:  \:  \:  \:  \:  \:  \:  \:  \: \: - 2m + 6 \:  \:  \:  \:   \:  \:  \:  \:\:}} \\{\sf{}}& \underline{\sf{\:\: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  2m - 6  \:  \:  \:  \:  \:  \: \:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \:  \: \:  \:  \:  0\:\:}}  \end{array}\end{gathered}\end{gathered}\end{gathered}$

Hence,

$\bf :\longmapsto\:\dfrac{ {m}^{2} - 5m + 6 }{m - 3} = m - 2$