Factor the equation???

Question

x cubed minus 8.....in other words
x3-8
^ it means x cubed
I cannot factor the equation!!!! plz help!!!

Answer 1

Hi,

x³ - 8 = (x - 2)(x² + 2x + 4)

Now we're going to look at the sum and difference of perfect cubes. Again always look first for a GCF. If there is one, factor it out. Perfect cube problems will always factor into a binomial times a trinomial, like this:

x³ + 125 = (x + 5)(x² - 5x + 25)

The general rule for these is:

1) Factor out a GCF if there is one.
2) Make 2 parentheses for a binomial and a trinomial.
3) The sign from the problem goes in the binomial. The opposite sign from what you just used goes in the trinomial, and is always followed by a "+" as the second sign in the trinomial. This is the only step where what you do is different on the sum of cubes from on the difference of cubes.
4) Figure out what you would cube to get the first term of the problem and put that expression as the first term of your binomial. Then figure out what you would cube to get the second term of the problem and put that expression as the second term of your binomial.
5) Your trinomial already has its signs, so don't worry about the signs. To find terms of the trinomial, write the first term of your binomial 3 times followed by the second term of your binomial 3 times out to the side. Multiply the first 2 things together to get the trinomial's first term. Multiply the next 2 things together to get the trinomial's middle term. Multiply the last 2 things together to get the trinomial's third term.

So for, x³ - 8, there is no GCF.
Parentheses would be ( - )( + + )
To get x³, you'd cube x.
To get 8, you'd cube 2.
So your binomial becomes (x - 2)( + + )
Now write x x x 2 2 2
x*x = x²
x*2 = 2x
2*2 = 4
So your trinomial becomes (x - 2)(x² + 2x + 4)

Here's another example:

So for 8x³ + 27y³, there is no GCF
Parentheses would be ( + )( - + )
To get 8x³, you'd cube 2x.
To get 27y³, you'd cube 3y.
So your binomial becomes (2x + 3y)( - + )
Now write 2x 2x 2x 3y 3y 3y
2x*2x = 4x²
2x*3y = 6xy
3y*3y = 9y²
So your trinomial becomes (2x + 3y)(4x² - 6xy + 9y²)

I hope that helps!! :-)

Answer 2

factoring is simplifying a equation... x²+8x+12 so which you're able to take the climate of 12: a million,12 2,6 3,4 then you definately locate the pair that provides to grant you 8. subsequently its 2 and six. so that then you definately write (x+6)(x+2)

Answer 3

x^3 - 8 = x^3 - 2^3

Difference of cubes

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

x^3 - 8 = (x - 2)(x^2 + 2x + 4)

Answer 4

x^3 - 8
= x^3 - 2^3
= (x - 2)(x^2 + 2x + 4)

Answer 5

x^3-8

(x-2)(x^2+2x+4)