how do you factorize x^4+27x

Question

zepdrix · Answer

Hey Angela!
They've both got some x's... factor those out first.$$\large\rm x^4+27x=x(x^3+27)$$From there you want to utilize your `Sum of Cubes Formula`:
$\large\rm a^3+b^3=(a+b)(a^2-ab+b^2)$

zepdrix · Answer

Hmm but we only have one thing being cubed... x.
If you can find a way to rewrite 27 as a perfect cube, you can apply this formula!

angelab97 · Answer

but how do you get (a+b)(a^2-ab+b^2) from x(x^3+27)? @zepdrix

zepdrix · Answer

You get $\large\rm (a+b)(a^2-ab+b^2)$ from $\large\rm a^3+b^3$
and you get $\large\rm a^3+b^3$ from $\large\rm x^3+27$

zepdrix · Answer

the x^3 matches up with the a^3, it's in the correct format.
But we need to rewrite 27 as $\large\rm something^3$

zepdrix · Answer

Example: $\large\rm 8=2\cdot2\cdot2$ therefore $\large\rm 8=2^3$
We found a way to write 8 as a perfect cube!
Can you find a way to do that with 27?

angelab97 · Answer

thank you!