Question

How do you factor `x^3+6x^2-5x-30`?

Answer 1

`x= -6, x=` `+-` `sqrt`5

Explanation:

rearrange the equation
`x^3 - 5x + 6x^2 - 30`

take out the common factors
`x(x^2 -5) +6(x^2 - 5)`

compress the terms
`(x+6)(x^2 - 5)`

solve for `x`
`x= -6, x=` `+-` `sqrt`5

Answer 2

`(x+6)(x-sqrt5)(x+sqrt5)`

Explanation:

`color(blue)"factor by grouping the terms"`

`=color(red)(x^2)(x+6)color(red)(-5)(x+6)`

`"take out the "color(blue)"common factor "(x+6)`

`=(x+6)(color(red)(x^2-5))`

`x^2-5" can be factored using "color(blue)"difference of squares"`

`a^2-b^2=(a-b)(a+b)`

`x^2-5=x^2-(sqrt5)^2`

`"with "a=x" and "b=sqrt5`

`rArrx^2-5=(x-sqrt5)(x+sqrt5)`

`rArrx^3+6x^2-5x-30=(x+6)(x-sqrt5)(x+sqrt5)`