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?
On
a. Mia could check her work by multiplying out her answer and seeing if she gets the original polynomial back. In her case
$$4x(2x-0)=8x^2-0=8x^2$$
which is wrong.
b. Mia did try to factor out $4x$: she just did it badly. She factored the last term, $+4x$, as $4x\cdot 0$, but it should have been $4x\cdot 1$.
c. The GCF is $4x$, so we get
$$8x^2+4x=4x\cdot 2x+4x\cdot 1=4x(2x+1)$$
In (c) you did not factor out all you could.
(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.