Question

Use the grouping method to factor the polynomial below completely.
x3 - 3x2 + 5x - 15

Answer 1

x^3 - 3x^2 + 5x - 15
x^2(x-3) +5(x-3)
(x^2 + 5)(x - 3) <==Answer

Answer 2

`(x^2+5)*(x-3)`

Explanation:

In grouping method factoring, you must have to split the middle term in a way that the product of two terms in middle must be equal to the product of two terms at the edges of equation. Remember you have to consider the resultant signs as well as the magnitude of both products.

Now in the case given above,

`x^3-3x^2+5x-15`

the result is
`-15x^3`

Note that the magnitude is 15x^3 and sign is '-' for both products.

Now taking out the common terms, equation becomes;

`x^2(x-3)+5(x-3)`

Taking out (x-3) as common, now the factorized version we have is:

`(x-3)(x^2+5)`