How do you factor 2x^3-1252x3−125?
1 Answer
Explanation:
The difference of cubes identity can be written:
a^3-b^3 = (a-b)(a^2+ab+b^2)a3−b3=(a−b)(a2+ab+b2)
Note that
We can treat it as a cube by using irrational coefficients, to find:
2x^3 = (root(3)(2)x)^32x3=(3√2x)3
and hence:
2x^3-125 = (root(3)(2)x)^3-5^32x3−125=(3√2x)3−53
color(white)(2x^3-125) = (root(3)(2)x-5)((root(3)(2)x)^2+(root(3)(2)x)(5)+5^2)2x3−125=(3√2x−5)((3√2x)2+(3√2x)(5)+52)
color(white)(2x^3-125) = (root(3)(2)x-5)(root(3)(4)x^2+5root(3)(2)x+25)2x3−125=(3√2x−5)(3√4x2+53√2x+25)
...noting that we have used
(root(3)(2))^2 = root(3)(2^2) = root(3)(4)(3√2)2=3√22=3√4
