Question 291734
{{{18z+45+z^2}}}. Please help me factor
<pre><font size = 4 color = "indigo"><b>
Rearrange terms in descending order:

{{{z^2+18z+red(45)}}}

Write down all pairs of positive integers which have product 45:

1*45=45
3*15=45
 5*9=45
 
{{{z^2+18z}}}{{{red("+")}}}{{{45}}}

Since the last sign is {{{red("+")}}}, out beside those pairs,
write their sum
 
1*45=45   1+45=46
3*15=45   3+15=18
 5*9=45    5+9=15

{{{z^2+red(18)z+45}}}

Look for the red {{{red(18)}}} among them. 

We find it at the pair of factors 3 and 15,
so we write

(x   3)(x   15)

Since the last term of {{{z^2+18z+45}}} is
positive, the signs are like and are the
same as the sign of the middle term {{{""+18z"}}}
So the factorization is

(x + 3)(x + 15)

Edwin</pre>