Question

Can `y=x^3-3x^2-10x` be factored? If so what are the factors ?

Answer 1

`y=x(x-5)(x+2)`

Explanation:

Take x out as a factor first to give:

`y=x(x^2-3x-10)`

Then factorise the quadratic in the brackets to give the answer above.

Answer 2

`y=x(x-5)(x+2)`

Explanation:

Inspection reveals that all three terms have `x` common in the given polynomial
`y=x^3-3x^2-10x` .....(1)

LHS can be written as
`x(x^2-3x-10)`

The quadratic in the brackets can be factorized by splitting the middle term
`(x^2-3x-10)`
`=>(x^2-5x+2x-10)`
`=>(x[x-5]+2[x-5])`
`=>([x-5][x+2])`

Hence factors are

`y=x(x-5)(x+2)`

Answer 3

`y = x(x-5)(x+2)`

Explanation:

Take out the common factor of `x` first:

`y = x^3 -3x^2 -10x`

`y = x(x^2-3x-10)`

To factorise the quadratic trinomial, find factors of `10` which subtract to give `3`

`15xx2 = 10 and 5-2 =3` so these are the factors we need.

Their signs must be different, but there must be more negatives.
This gives:

`y = x(x-5)(x+2)`