Question

How do you factor `7x^2+5x-2`?

Answer 1

`(7x-2)(x+1)`

Explanation:

`7x^2` only has `7x and x` as factors
-2 is `2xx1` with one of them negative.

Answer 2

`(x+1)(7x-2)`

Explanation:

Multiply the coefficient by the constant:

`7 xx -2=-14`

Replace it as the new constant:

`-> 7x^2+5x-14`

Find the numbers:

`7-2=5`

`7xx-2=-14`

So these work.

Substitute these in:

`7x^2+7x-2x-2` `color(blue)(lArr "Notice we replaced the 14 with 2")`

Factorise the first two expressions:

`7x^2+7x -> 7x(x+1)`

Factorise the next two expressions:

`-2x-2`

`-2(x+1)` `color(blue)(lArr "Notice the brackets are the same")`

Therefore we get:

`color(red)(7x)color(green)((x+1))color(red)(-2)color(green)((x+1))`

One bracket is `(x+1)` and the other bracket is the remaining terms:

`-> (7x-2)`

We can always check by expanding:

`(7x-2)(x+1)=7x^2+7x-2x-2`

`-> 7x^2+5x-2`

Which is the original, so we are correct.