Methods for verifying correct factorisation of polynomials In an attempt to factor using a GCF, Mia wrote $8x^2 + 4x = 4x(2x – 0)$, which is not correct.
a. Explain how Mia could check her work.
b. What error did Mia make?
She didn't factor using the GFC which is $4x$.  
c. Show the correct factorization of $8x^2 + 4x$.
$2^3 x^2 + 2^2 x$
$4(2x^2+x)$
I am not certain that I'm going at this question the right way. Also, how do I go about checking her work? 

(a) You can simply plug values for $x$ into the expression and the false factorised expression. For example $x=2$ gives two different results, so the factorised expression is wrong. 
(b) Correct. 
(c) You can pull out another $x$ to get $$4(2x^2 + x) = 4x(2x + 1)$$
Which is the fully factorised form. 
