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Factoring a Cubic Function

  • #1
Alright, so I need a little brush up on my pre calc apparently! I need to determine the x-intercepts of the following function.

y=x^3 + 2

I know I need to factor it... I'm just not completely sure how! Thanks!
 

Answers and Replies

  • #2
172
2
There's no need to factor. The x-intercepts are when y=0, so you just need to solve the equation:

[itex]0=x^3+2[/itex]
 
  • #3
Mentallic
Homework Helper
3,798
94
Calcuconfused, If you move the 2 onto the other side of [itex]0=x^3+2[/itex] and then take the cube root of both sides, you'll end up with [tex]x=-\sqrt[3]{2}[/tex] so if you were to try and factor it (in case you need to find the factors for another purpose, such as to show what all 3 roots are) you're going to have an ugly thing to factor.

But regardless, if you need to factor it, you'll end up with a linear factor and a quadratic factor, and since we've already shown one of the roots, the end result will be of the form

[tex]\left(x+\sqrt[3]{2}\right)\left(x^2+ax+\sqrt[3]{4}\right)[/tex]

For some yet to be found constant value a.
 

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