How do you factor $8 x^{4} + x$ $8x^4+x$ ?

Question

6130 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-12T21:44:21

$x (2 x + 1) (4 x^{2} - 2 x + 1)$ $x(2x+1)(4x^2-2x+1)$

List factors of both terms.

$8 x^{4} = 8 \cdot x \cdot x \cdot x \cdot x$ $8x^4 = 8*color(orange)(x)*x*x*x$

$x = x$ $x=color(orange)(x)$

The common factors are just one $x$ $color(orange)(x)$ .
So let's pull out one $x$ $x$ from the expression.

$x (8 x^{3} + 1)$ $color(orange)(x)(8x^3+1)$

We still need to factor $(8 x^{3} + 1)$ $(8x^3+1)$ . Take note that $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ $a^3+b^3 = (a+b)(a^2-ab+b^2)$ .

$x (2 x + 1) (4 x^{2} - 2 x + 1)$ $x(2x+1)(4x^2-2x+1)$

How do you factor 8x4+x8x^4+x ?