Question

How do you factor `56x^3+70x^2-280x-350`?

Answer 1

`56x^3+70x^2-280x-350=14(x-sqrt(5))(x+sqrt(5))(4x+5)`

Explanation:

Separate out the common scalar factor `14`, factor by grouping and finally use the difference of squares identity:

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

with `a=x` and `b=sqrt(5)` as follows:

`56x^3+70x^2-280x-350`

`=14(4x^3+5x^2-20x-25)`

`=14((4x^3+5x^2)-(20x+25))`

`=14(x^2(4x+5)-5(4x+5))`

`=14(x^2-5)(4x+5)`

`=14(x^2-(sqrt(5))^2)(4x+5)`

`=14(x-sqrt(5))(x+sqrt(5))(4x+5)`