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

Answer:

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

Step-by-step 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 $(x^2 + 7)(x- 4)$