Question 316254
Hello. I need to find the greatest common divisor of:

{{{3y^3-27y}}}  and {{{6y^3)+12y^2-90y}}}

I know to pull out 3y from the first expression to get:

{{{3y(y^2-9)}}}.
<pre><font color = "red"><b>
Right there you need to factor the {{{red((y^2-9))}}} as {{{red((y-3)(y+3))}}}
and get:

{{{red(3y(y-3)(y+3))}}}.
</font></pre></b>
and 6y from the second expression to get:

{{{6y(y^2+2y-15)}}}

<pre><font color = "red"><b>
Right there you need to factor the {{{red((y^2+2y-15))}}} as {{{red((y-3)(y+5))}}}
and get:

{{{red(6y(y-3)(y+5))}}}

So you have to get the GCD of

{{{red(3y(y-3)(y+3))}}} and {{{red(6y(y-3)(y+5))}}}

They have factors {{{red(3)}}}, {{{red(y)}}}, and {{{red((y-3))}}} in common.

So the GCF is {{{3y(y-3)}}} which when multiplied out gives {{{3y^2-9y}}}

Edwin</pre></font></b>