Question

Find the imaginary or real solutions of the equation by factoring
X^3+64=0

Answer 1

Hi :)
Welcome to openstudy!
Any ideas on what the first step maybe?

Answer 2

No. I'm not sure how to factor numbers like this one

Answer 3

Ok well similar to difference of 2 squares we can start by subtract 64 from both sides
\[\huge~\rm~x^3+64-63=0 -64\]

Answer 4

Now we have
\[\huge~\rm~\bf~x^3=-64\]
Now you would take the cube root are you familiar with how to do that?

Answer 5

Of I had a calculator

Answer 6

Or without a calculator

Answer 7

That's one good approach c:
It looks like they want us to solve this one by factoring though.


Recall your `Sum of Cubes` Formula:\[\large\rm a^3+b^3=(a+b)(a^2-ab+b^2)\]

Answer 8

I didn't see they wanted it by factoring sorry im not familiar with that method @zepdrix seems to be good at it perhaps he can continue with the problem :-)

Answer 9

64 is actually a perfect cube,
64 = 4*4*4
So we can rewrite our expression,\[\large\rm x^3+64\]as\[\large\rm x^3+4^3\]From there, we can apply our `Sum of Cubes` Formula

Answer 10

Okay, so I find the cube, and then re-write it.

Answer 11

Applying the formula gives us this,\[\large\rm x^3+4^3=(x+4)(x^2-4x+4^2)\]
I'll give you a moment to digest that,
look back at the formula involving a and b for reference.

Answer 12

I don't get how to use the formula. I've never seen it in my life

Answer 13

Have you ever heard the acronym SOAP?
It's often used as a nice easy way to remember this formula.

Answer 14

No I have not. My math teacher doesn't put any description in his online lessons. He kind of just expects us to understand everything

Answer 15

This is where our SOAP acronym comes from.