How do you factor the expression #2x^4 + 16x#?

Question

3014 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-10T09:49:54

#2x^4+16x=2x(x+2)(x^2-2x+4)#

The idea is to transform the expression in a form where you can use the remarkable factorization identities.

Here we can use Factoring by Grouping to obtain:

#2x^4+16x=color(green)(2x)(x^3+8)=2x(x^3+2^3)#

Now, the second factor is a sum of cubes, then we can use the following identity:

#(a^3+b^3)=(a+b)(a^2-ab+b^2)#

where:

#a=x, b=2#

#:.2x(x^3+2^3)=2xcolor(green)((x+2)(x^2-x*2+2^2))=#
#=2x(x+2)(x^2-2x+4)#

No more factorization allowed