Question 108815
The first thing that you do when factoring is take out all of the {{{Greatest- Common- Factor}}}

Example:

{{{6x³+27x²-105x}}}………..when factor the numbers {{{6}}}, {{{27}}}, and
 
{{{105}}}, you will see that each one is divisible by {{{3}}}. 

Also, when you look at {{{x^3}}}, {{{x^2}}}, and {{{x}}}, you will see that 

all of them you can divide by {{{x}}}

So, the {{{greatest- common- factor}}} here is {{{3x}}}.

Then you can write your equation like this:

{{{3x(2x^2 + 9x - 35)}}}


Then you factor {{{(2x^2 + 9x - 35)}}}.

{{{(2x^2 + 9x - 35)}}}….write {{{9x}}} as {{{14x - 5x}}}

{{{(2x^2 + 14x - 5x - 35)}}}……..group first and third term, second and fourth term

{{{(2x^2 - 5x)}}} + ({{{14x}}} – {{{35}}})……..here, in first term common factor is 
{{{x}}}, and in second term common factor is {{{7}}}

so, we can write it: {{{x(2x-5)}}}, and {{{7(2x-5)}}} where we see that common 

factor is {{{2x – 5}}}

now we can write {{{(2x-5)(x + 7)}}}

if we go back to our equation, we can write it like this:

{{{3x(2x-5)(x+7)}}}

Remember:

Factoring a polynomial is the {{{opposite }}}{{{process }}}of multiplying polynomials.

The {{{simplest}}} type of factoring is {{{when}}}{{{ there}}}{{{ is}}} a factor {{{common}}}{{{ to}}}{{{ every}}}{{{ term}}}.

Recall that the {{{distributive}}}{{{ law}}} says that {{{a(b + c) = ab + ac}}} 

If you see something of the form {{{a2 - b2}}}, you should remember the formula: 
{{{(a-b)(a+b)}}}={{{a^2}}} – {{{b^2}}}


This only holds for a {{{difference}}} of two squares, NOT for a {{{sum}}} of two squares such as{{{ a2 + b2}}}into factors with real numbers.

Remember:

 “Perfect Square Trinomial”
Recall from special products of binomials that {{{(a + b)^2 = a^2 + 2ab + b^2}}} and{{{(a - b)^2 = a^2 - 2ab + b^2}}}

It will help you to solve any problem. Good luck!!!!!!!!!