How do you factor 2x^3+16 2x3+16?

1 Answer
Aug 25, 2016

2(x^3+8) = 2(x+2)(x^2-2x+4)2(x3+8)=2(x+2)(x22x+4)

Explanation:

Always look for a common factor first.

Both terms can be divided by 2.

2(x^3+8)2(x3+8)

Both x^3 and 8x3and8 are cube numbers. The sum or difference of cubes can be factored according to:

(a^3 + b^3) = (a+b)(a^2 -ab + b^2)(a3+b3)=(a+b)(a2ab+b2)
(a^3 - b^3) = (a+b)(a^2 +ab + b^2)(a3b3)=(a+b)(a2+ab+b2)

2(x^3+8) = 2(x+2)(x^2-2x+4)2(x3+8)=2(x+2)(x22x+4)