Factor a^2 - 5a + 8

Step by step

The question

Question: factor completely a² − 5a + 8.

Completely means: until no part can be factored any more.

1 Common factor first

Always ask this first.

Here no number and no a goes into every term.

So there is no common factor.

2 Count the terms

The bracket has 3 terms.

With 3 terms we look for two numbers that multiply to c and add to b.

3 Prime or not

We need two numbers.

They multiply to 8, and they add to −5.

We list every pair that makes 8.

We add each pair.

We need 5.

None of them gives 5.

No pair works.

So a² − 5a + 8 does not factor with whole numbers.

We call it prime.

So a² − 5a + 8 is prime.

Let's look back.

First: common factor first.

Then: count the terms.

Last: prime or not.