Question 116128
1. {{{x^3 - 26x^2 + 48x }}}……notice that {{{x}}} is common in all three terms, factor it out

{{{x(x^2 - 26x + 48) }}}………replace {{{- 26x}}} with the two numbers that multiply to {{{48}}} and add to {{{-26}}}, which are: {{{-2}}} and {{{-24}}} 

{{{x(x^2 - 2x - 24x + 48) }}}………group the first two terms together and the last two terms together 

{{{x((x^2 - 2x) +( - 24x + 48)) }}}………factor a {{{1x}}} out of the first group and factor a {{{-24}}} out of the second group

{{{x(1x(x - 2) -24( x - 2)) }}}………now we have a common term {{{x – 2}}} we can combine the two terms

{{{x(x -24)( x - 2) }}}………this is your answer


2. 

{{{x^2 - 6wy + 3xy -2 wx }}}

{{{(x^2 + 3xy) + ( -2 wx- 6wy ) }}}

{{{x(x+ 3y) -2w ( x + 3y ) }}}……………. combine the common terms

{{{x(x -2w) ( x + 3y ) }}}…………….


3. 

{{{x^2 -5x - 14 }}}

{{{x^2 -5x - 14 }}}……….replace {{{-5x}}} with the two numbers that multiply to {{{-14}}} and add to {{{-5}}}, which are {{{ 2}}} and {{{-7}}}

{{{x^2 + 2x -7x - 14 }}}……….group the first two terms together and the last two terms together

{{{(x^2 + 2x)+(-7x - 14) }}}……….Factor a {{{x}}} out of the first group and factor a {{{-7}}} out of the second group

{{{x(x + 2)- 7( x + 2) }}}………combine the common terms

{{{x(x - 7) ( x + 2 ) }}}…………….



4. 

{{{4x^2 - 36y^2}}}………..notice that you can write {{{4}}} as a {{{2^2}}} and {{{36}}}as a {{{6^2}}}

{{{2^2*x^2 -6^2*y^2}}}..............we can write {{{6^2}}} as {{{2^2*3^2}}}

{{{2^2*x^2 -2^2*3^2*y^2}}}..............factor out common {{{2^2}}}

{{{2^2(x^2 -3^2*y^2)}}}.............

{{{2^2(x^2 -(3y)^2)}}}.............notice the difference square numbers, apply rule for it

{{{4(x -3y)(x+3y)}}}.............