# How do you factor y=(5x+2)^2 + 11(5x+2)+30 ?

Jan 18, 2016

$\textcolor{g r e e n}{y = \left(5 x + 7\right) \left(5 x + 8\right)}$

Have a look at the 'trick' I used!

#### Explanation:

Multiply out the brackets so that you can collect like terms and simplify:

Let $\left(5 x + 2\right)$ be z then we have

$y = {z}^{2} + 11 z + 30$

Factors of 30 are: {1,30} ; {2, 15} ; {3,10} ; {5,6}

We observe that 5+6=11 so we try those first:

$y = \left(z + 5\right) \left(z + 6\right) = {z}^{2} + 6 z + 5 z + 30 \textcolor{red}{\text{ This works}}$

Substitute back for z giving:

$y = \left[\left(5 x + 2\right) + 5\right) \left(\left[5 x + 2\right] + 6\right)$

$\textcolor{g r e e n}{y = \left(5 x + 7\right) \left(5 x + 8\right)}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check by multiplying out the brackets

$y = \left(5 x + 7\right) \left(5 x + 8\right)$

$y = 25 {x}^{2} + 40 x + 35 x + 56 \textcolor{w h i t e}{\ldots} = 25 {x}^{2} + 75 x + 56 \textcolor{red}{\text{ This works}}$