Step by step
The question
Question: factor 2x² + 7x + 3.
Factor means: write it as a times, with brackets.
1 Find two numbers
The number in front of x² is 2.
So we multiply 2 by 3: that is 6.
We need two numbers that multiply to 6 and add to 7.
They multiply to a plus number, so the two numbers have the same sign.
They add to a plus number, so both are plus.
We list the pairs that make 6, smallest first.
We add each pair.
We need 7.
1 and 6 give 7.
Yes!
2 Split the middle
We write 7x as x + 6x.
It is the same amount.
3 Group in pairs
We put the first two together, and the last two together.
From the first pair we take out x.
From the second pair we take out 3.
Both leave the same bracket.
Now both parts have 2x + 1 in them.
4 Same bracket out
2x + 1 is in both parts, so we take it out once.
What is left, x + 3, goes in the other bracket.
So we get (2x + 1)(x + 3).
5 Check
Let's check: we multiply it back out.
Each part of the first bracket times each part of the second.
We get 2x² + 7x + 3 again.
So (2x + 1)(x + 3) is right!
Let's look back.
First: find two numbers.
Then: split the middle.
Then: group in pairs.
Then: same bracket out.
Last: check.