Question

f (x) = 8x^4 – 64

Factor completely

Answer 1

Answer:

8(x^4 - 8)

Step-by-step explanation:

Factor out an 8, since both 8 and 64 are divisible by 8:

f(x) = 8x^4 - 64

f(x) = 8(x^4 - 8)

So, the equation factored completely is 8(x^4 - 8)

Answer 2

Answer:

$\huge\boxed{f(x)=8(x-\sqrt[4]8)(x+\sqrt[4]8)(x^2+2\sqrt2)}$

$\huge\boxed{f(x)=8(x-2)(x^2+2x+4)}$

Step-by-step explanation:

$f(x)=8x^4-64\qquad|\text{distribute}\\\\f(x)=8(x^4-8)=8\bigg[(x^2)^2-\left(\sqrt8\right)^2\bigg]\qquad|\text{use}\ (a-b)(a+b)=a^2-b^2\\\\f(x)=8(x^2-\sqrt8)(x^2+\sqrt8)=8\bigg[x^2-\left(\sqrt[4]8\right)^2\bigg](x^2+\sqrt8)\\\\|\text{use}\ (a-b)(a+b)=a^2-b^2\\\\f(x)=8(x-\sqrt[4]8)(x+\sqrt[4]8)(x^2+\sqrt8)\\\\\sqrt8=\sqrt{4\cdot2}=\sqrt4\cdot\sqrt2=2\sqrt2$

taking into account the correction from the comment

$f(x)=8x^3-64=8(x^3-8)=8(x^3-2^3)\\\\\text{use}\ a^3-b^3=(a-b)(a^2+ab+b^2)\\\\f(x)=8(x-2)(x^2+(x)(2)+2^2)=8(x-2)(x^2+2x+4)$