Question

How do you factor the expression `3x^2 + 3 + x^3 + x`?

Answer 1

`color(magenta)(=(3+x)(x^2+1)`

Explanation:

`3x^2+3+x^3+x`

Grouping the `1^(st)` `2` terms together and the `2^(nd` `2` together, we get:

`=3(x^2+1)+x(x^2+1)` (taking out common factors)

`color(magenta)(=(3+x)(x^2+1)`

~Hope this helps! :)

Answer 2

`(x^2+1)(3+x)`

Explanation:

`"factorise in 'groups'"`

`[3x^2+3]+[x^3+x]`

`=color(red)(3)(x^2+1)color(red)(+x)(x^2+1)`

`"take out the "color(blue)"common factor "(x^2+1)`

`=(x^2+1)(color(red)(3+x))`

`rArr3x^2+3+x^3+x=(x^2+1)(3+x)`