Factor completely 5x^2 - 5 Step by Step

Step by step

The question

Question: factor completely 5x² − 5.

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

5x² − 5

1 Common factor first

All the numbers can be divided by 5.

So the common factor is 5.

5, 5: all in the 5 times table

We divide every term by it.

What is left goes in the bracket.

5x² ÷ 5 = x²

−5 ÷ 5 = −1

So it is 5(x² − 1).

= 5(x² − 1)

2 Count the terms

The bracket has 2 terms.

With 2 terms we look for two squares or two cubes.

x² − 1 is one square take away another square.

x² is x squared.

1 is 1 squared.

A square minus a square is the plus bracket times the minus bracket.

a² − b² = (a + b)(a − b)

x² = (x)², 1 = 1²

So we get 5(x + 1)(x − 1).

= 5(x + 1)(x − 1)

3 Check each bracket

Brackets like x + 1 have just x and a number.

They can't be factored.

x + 1, x − 1: just x and a number

No bracket can be factored any more.

So we are done.

Careful!

Don't forget the common factor 5 in the answer.

Careful: not (x² − 1) ✗

4 Check

Let's check: we multiply it back out.

Each part of one bracket times each part of the other.

Check: (x + 1)(x − 1) = x² − x + x − 1

= x² − 1

Then the common factor times every part.

5(x² − 1) = 5x² − 5

We get 5x² − 5 again.

So it is right!

Let's look back.

First: common factor first.

Then: count the terms.

Then: check each bracket.

Last: check.

Answer