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

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Answer 1 · 2016-05-17T11:09:53

$(x+3)(5x+6)$

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

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

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

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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 $a" as "(x+3)"$

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

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