Question

Factor x- 4x' + 7x- 28 by grouping. What is the resulting expr

O (- 4)(x + 7)
O +4)(x - 7)
O (x2-7)(x + 4)
O +7)(x- 4)

Answer 1

`(x^2 + 7)(x- 4)`

Explanation:

Given

`x^3 - 4x^2 + 7x - 28`

Required

Factorize by grouping

`x^3 - 4x^2 + 7x - 28`

Expand the given expression into 2 parts

`[x^3 - 4x^2] + [7x - 28]`

Factorize each group:

`[x^2(x - 4)] + [7(x - 4)]`

Remove square brackets

`x^2(x - 4) + 7(x - 4)`

This gives:

`(x^2 + 7)(x- 4)`

Hence, the factored form of
`x^3 - 4x^2 + 7x - 28` is
`(x^2 + 7)(x- 4)`