Factor x^2 - 10x + 25

Step by step

The question

Question: factor x² − 10x + 25.

Factor means: write it as a times, with brackets.

1 Find two numbers

We need two numbers.

They multiply to 25, and they add to −10.

They multiply to a plus number, so the two numbers have the same sign.

They add to a minus number, so both are minus.

We list the pairs that make 25, smallest first.

We add each pair.

We need 10.

5 and 5 give 10.

Yes!

With the signs: −5 and −5.

The two numbers go in the brackets.

So we get (x − 5)(x − 5).

The same bracket twice.

So we write it as (x − 5)².

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 − 10x + 25 again.

So (x − 5)(x − 5) is right!

Let's look back.

First: find two numbers.

Last: check.