enriquezbea46 enriquezbea46
  • 23-02-2022
  • Mathematics
contestada

given that (x-2) is a factor of (x³-8) ,what is the other factor?​

Respuesta :

iciclepiano18
iciclepiano18 iciclepiano18
  • 23-02-2022

Answer:

[tex]x^2+2x+4[/tex]

Step-by-step explanation:

This expression can also be written as a difference of cubes:

[tex]x^3-2^3[/tex]

A important formula to remember is:

[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]

We can use this to factor this expression:

[tex]x^3-2^3=(x-2)(x^2+2x+4)[/tex]

Therefore the other factor is:

[tex]x^2+2x+4[/tex]

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