Question

Factorize the following: x+9x+14, z-3z+2, r-25, a-14a+49, t-t-12

Answer 1

I assume these are all quadratics, or there'd be no need to factorize them.
Consider x^2 + 9x + 14
You know that (x+a)(x+b) = x^2 + (a+b)x + ab
so you have to ask yourself:
which two factors of 14 add up to 9? 2 and 7
So, x^2+9x+14 = (x+2)(x+7)

Now work the others the same way.
Note that for t^2-t-12, since -12 is negative,
you have to ask yourself: which two factors of 12 differ by 1?
But they add up to -1, so use -4 and 3.

Now you try the others; come back with your work if you get stuck.