My mind is coming to a blank as to how to factor out this polynomial:
27x^3 - 8
Any help is greatly appreciated!! :D
Never mind, I think I just got it xD is this what it looks like factored out?
(x - 2/3)(x^2 + [2/3] + 12)
grrr i mean [2/3]x in the middle of the second equation
You're close.
x³-y³
=(x-y)(x²+xy+y²)
Can you take it from here?
Omg. I feel like an idiot *bangs head against wall*. Soooo it would be (3x-2)(9x²+2x+4)?
Exactly!
To factor out the polynomial 27x^3 - 8, we can use the difference of cubes formula. The difference of cubes formula states that for any two numbers a and b, we can factor the expression a^3 - b^3 as (a - b)(a^2 + ab + b^2).
In this case, a is 3x and b is 2. So, we can rewrite 27x^3 as (3x)^3 and 8 as 2^3. Now we can apply the difference of cubes formula:
27x^3 - 8 = (3x)^3 - 2^3
Substituting a = 3x and b = 2:
= (3x - 2)((3x)^2 + (3x)(2) + 2^2)
Simplifying further:
= (3x - 2)(9x^2 + 6x + 4)
And there you have it! The factored form of 27x^3 - 8 is (3x - 2)(9x^2 + 6x + 4).