Answer:
[tex](x^2 + 7)(x- 4)[/tex]
Step-by-step explanation:
Given
[tex]x^3 - 4x^2 + 7x - 28[/tex]
Required
Factorize by grouping
[tex]x^3 - 4x^2 + 7x - 28[/tex]
Expand the given expression into 2 parts
[tex][x^3 - 4x^2] + [7x - 28][/tex]
Factorize each group:
[tex][x^2(x - 4)] + [7(x - 4)][/tex]
Remove square brackets
[tex]x^2(x - 4) + 7(x - 4)[/tex]
This gives:
[tex](x^2 + 7)(x- 4)[/tex]
Hence, the factored form of [tex]x^3 - 4x^2 + 7x - 28[/tex] is [tex](x^2 + 7)(x- 4)[/tex]
