Respuesta :

[tex](a+4)^2 -11(a+4) -42\\\\=x^2 -11x -42~~~~~~~~~~~~~~~~~~~~~~~~;[a+4 = x]\\\\=x^2 -14x +3x -42\\\\=x(x-14) +3(x-14)\\\\=(x+3)(x-14)\\\\=(a+4+3)(a+4-14)~~~~~~~~~~~~;[\text{Substitute back}~ a+4 =x]\\\\=(a+7)(a-10)[/tex]

Answer:

(a - 10) (a + 7)

Step-by-step explanation:

⠀⠀⠀⠀□ Question

(a + 4)² - 11(a + 4) - 42

Fractorize

⠀⠀⠀⠀■ Solution

  • Let (a + 4) = x

So the equation will be

[tex] \sf \large {x}^{2} - 11x - 42[/tex]

  • Using spitting the middle term method.

[tex] \sf {x}^{2} - 14x + 3x - 42[/tex]

  • Taking common

[tex] \sf x(x - 14) + 3(x - 14)[/tex]

[tex] \sf (x - 14)(x + 3)[/tex]

  • Putting value of 'x'

[tex] \sf (a + 4 - 14)(a + 4 + 3) \\ \\ \boxed{ \frak{(a - 10)(a + 7)} } [/tex]