Question

How do you factor completely `5x(x + 3) + 6(x + 3)`?

Answer 1

`(x+3)(5x+6)`

Explanation:

They have already done a lot of the work for you.

The common factor is `(x+3)` so we factor that out giving:

`color(blue)((x+3))color(brown)((5xcolor(green)(+)6))`

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To emphasise how this works:

Consider the example `color(blue)(a)color(brown)((b color(green)(+)c))`

This is saying multiply everything inside the brackets by `a`.

So you have `color(brown)(color(blue)(a xx)b color(green)(+)color(blue)(a xx)c)`

Notice that the `color(green)(+)` is still kept between.

now think of `a" as "(x+3)"`

`color(brown)(color(blue)((x+3)xx)5xcolor(green)(+)color(blue)((x+3)xx)6)`