Factor completely -2x^2 + 8 Step by Step

Step by step

The question

Question: factor completely −2x² + 8.

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

−2x² + 8

1 Common factor first

All the numbers can be divided by 2.

The first term is negative, so we take out a minus too.

So the common factor is −2.

2, 8: all in the 2 times table

We divide every term by it.

What is left goes in the bracket.

−2x² ÷ −2 = x²

8 ÷ −2 = −4

So it is −2(x² − 4).

= −2(x² − 4)

2 Count the terms

The bracket has 2 terms.

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

x² − 4 is one square take away another square.

x² is x squared.

4 is 2 squared.

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

a² − b² = (a + b)(a − b)

x² = (x)², 4 = 2²

So we get −2(x + 2)(x − 2).

= −2(x + 2)(x − 2)

3 Check each bracket

Brackets like x + 2 have just x and a number.

They can't be factored.

x + 2, x − 2: just x and a number

No bracket can be factored any more.

So we are done.

Careful!

Don't forget the common factor −2 in the answer.

Careful: not (x² − 4) ✗

4 Check

Let's check: we multiply it back out.

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

Check: (x + 2)(x − 2) = x² − 2x + 2x − 4

= x² − 4

Then the common factor times every part.

−2(x² − 4) = −2x² + 8

We get −2x² + 8 again.

So it is right!

Let's look back.

First: common factor first.

Then: count the terms.

Then: check each bracket.

Last: check.

Answer