Bomarie02
Bomarie02 Bomarie02
  • 03-10-2019
  • Mathematics
contestada

Which of the following is a factor of x^15 - 64

A) x^5 - 4
B) x^10 - 4x^5 + 16
C) x^10 - 4
D) x^15 + 8x + 16​

Respuesta :

jimrgrant1 jimrgrant1
  • 03-10-2019

Answer:

A

Step-by-step explanation:

[tex]x^{15}[/tex] - 64 ← is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²)

Hence

[tex]x^{15}[/tex] - 64

= ([tex]x^{5}[/tex])³ - 4³

= ([tex]x^{5}[/tex] - 4)([tex]x^{10}[/tex] + 4[tex]x^{5}[/tex] + 16)

Thus A is a factor

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