Step by step
The question
Question: factor x² + 5x + 6.
Factor means: write it as a times, with brackets.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Find two numbers
First, see how two brackets open.
(x + 2)(x + 4) gives x² + 4x + 2x + 8.
That is x² + 6x + 8.
2 and 4 multiply to make the last number, 8.
And they add to make the middle number, 6.
Factoring goes backwards.
We need two numbers.
They multiply to 6, and they add to 5.
They multiply to a plus number, so the two numbers have the same sign.
Plus times plus is plus, and minus times minus is plus.
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 5.
2 and 3 give 5.
Yes!
The two numbers go in the brackets.
So we get (x + 2)(x + 3).
2 Check
Let's check: we multiply it back out.
Each part of the first bracket times each part of the second.
We get x² + 5x + 6 again.
So (x + 2)(x + 3) is right!
3 Pick the choice
Our answer is (x + 2)(x + 3).
That is choice D.
4 Why not the others
A is (x + 1)(x + 6).
Wrong: 1 × 6 = 6, but 1 + 6 = 7, not 5.
B is (x + 5)(x + 1).
Wrong: 5 × 1 = 5, not 6.
C is (x − 2)(x − 3).
Wrong: −2 + (−3) = −5, not +5.
Let's look back.
First: find two numbers.
Then: check.
Then: pick the choice.
Last: why not the others.