I can factorize problems like this:
3x^2 + 5x
3x^2: (1) (3) (x) (x)
5x: (1) (5) (x)
Using 1 and x to drop outside and use the leftovers:
x(3x + 5) *final*
But I'm being stumped by this kind of problem:
(x + 2)^2 - 5(x + 2) ?
I can factorize problems like this:
3x^2 + 5x
3x^2: (1) (3) (x) (x)
5x: (1) (5) (x)
Using 1 and x to drop outside and use the leftovers:
x(3x + 5) *final*
But I'm being stumped by this kind of problem:
(x + 2)^2 - 5(x + 2) ?
First expand both sets of brackets:
$\displaystyle (x + 2)^2 - 5(x + 2) = x^2+4x+4-5x-10$
Collect like terms:
$\displaystyle x^2-x-6$
Then factorise like you would a normal quadratic equation (I am assuming that you have come across these before, if not please say).
Hope this helps.
Think about it like this:
$\displaystyle
(x + 2)^2 - 5(x + 2) ~=~ (x+2)\textcolor{red}{(x+2)} - (5)\textcolor{red}{(x+2)}
$
So, we see that $\displaystyle (x+2)$ is common in both terms, so we factor the whole thing out:
$\displaystyle \textcolor{red}{(x+2)} \left[ (x+2) - 5 \right]$
Then you can simplify the right half.