Question

How do you factor `x^2 = x + 2`?

Answer 1

`(x+1)(x-2)=0`

Explanation:

This question can be done in following way-

`x^2=x+2`

Now

`x^2-x-2=0`

So

`x^2-2x+x-2=0`

`x(x-2)+1(x-2)=0`

Now

`(x+1)(x-2)=0`

This is the solution.

Answer 2

`(x-2)(x+1)=0`

Explanation:

`"subtract "x+2" from both sides"`

`x^2-x-2=0larrcolor(blue)"in standard form"`

`"the factors of "-2" which sum to "-1`
`"are "-2" and "+1`

`(x-2)(x+1)=0`

Answer 3

`(x-2)(x+1)=0`

Explanation:

We have a second-degree term, so we know we're dealing with a quadratic. Let's set it equal to zero.

We can subtract the quantity `x+2` from both sides to get

`x^2-x-2=0`

We can factor this with a little thought experiment:

What two numbers sum up to `-1` (middle term) and have a product of the `-2` (last term)?

After some trial and error, we arrive at `-2` and `1`. This means we can factor this as

`(x-2)(x+1)=0`

Hope this helps!