Step by step
The question
Question: factor 4x² + 6x.
Factor means: write it as a times, with brackets.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Take out the common factor
A term is one part between the + and − signs.
A common factor goes into every term.
4 and 6 can both be divided by 2.
Every term has at least x.
So the common factor is 2x.
We divide every term by it.
What is left goes in the bracket.
So it is 2x(2x + 3).
2 Check
Let's check: we multiply it back out.
The term in front times each part.
We get 4x² + 6x again.
So 2x(2x + 3) is right!
3 Pick the choice
Our answer is 2x(2x + 3).
That is choice A.
4 Why not the others
B is 2x(2x + 6).
Wrong: 2x × 6 is 12x, not 6x.
C is 4x(x + 6).
Wrong: 4x × 6 is 24x, not 6x.
D is 2(2x² + 6x).
Wrong: 2 × 6x is 12x, not 6x.
Let's look back.
First: take out the common factor.
Then: check.
Then: pick the choice.
Last: why not the others.