How do you factor $16x^3 - 250$ ?

Question

4394 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-27T10:01:41

Separate out the common scalar factor $2$ , then use the difference of cubes identity to find:

$16x^3-250 = 2(2x-5)(4x^2+10x+25)$

Both $16$ and $250$ are divisible by $2$ so separate that out first.

$16x^3-250 = 2(8x^3-125)$

Now $8 = 2^3$ and $125 = 5^3$

So we find:

$2(8x^3-125)$

$=2((2x)^3-5^3)$

$=2(2x-5)((2x)^2+(2x)*5+5^2)$

$=2(2x-5)(4x^2+10x+25)$

...using the difference of cubes identity:

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

How do you factor 16x^3 - 25016x^3 - 250?