Question

How do you factor by grouping `x^3+4x^2+8x+32`?

Answer 1

`(x^2 + 8 )(x+4 )`

Explanation:

Factor each half of the expression individually first:

`=> x^2 color(blue)(( x + 4)) + 8color(blue)( ( x +4))`

Hence `(x+4)` is common in each term, factor this out:

`=> color(blue)(( x+4 )) [ x^2 + 8 ]`

`color(red)(= (x^2 + 8 ) ( x + 4)`

In terms of real numbers, this is factorised

Answer 2

`(x+4)(x^2+8)`

Explanation:

`=color(red)(x^2)(x+4)color(red)(+8)(x+4)`

`"take out the "color(blue)"common factor "(x+4)`

`=(x+4)(color(red)(x^2+8))`

`x^3+4x^2+8x+32=(x+4)(x^2+8)`