Please factor the following
x^3 + 27.
I cannot seem to grasp the concept
Thank you
a^3 + b^3 = (a+b)(a^2-ab+b^2)
so, x^3+3^3 = (x+3)(x^2-3x+9)
First, you can take the cubed root of x^3 to get x. Second, you can take the cubed root of 27 to get 3.
So, let's start by dividing x^3 + 27 by x + 3:
.......x^2 - 3x + 9
x + 3 )x^3 + 27
.......x^3 + 3x^2-->change signs
........... - 3x^2 + 27
........... - 3x^2 - 9x-->change signs
.....................9x + 27
.....................9x + 27-->change signs
...........................0-->no remainder
Factors are:
(x + 3) (x^2 − 3x + 9)
I hope this will help.
To factor the expression x^3 + 27, we can use the formula for factoring the sum of cubes. The formula states that a^3 + b^3 can be factored as (a + b)(a^2 - ab + b^2).
In this case, we have x^3 + 27. We can rewrite 27 as 3^3, so the expression becomes x^3 + 3^3.
Now, comparing this to the formula, we have a = x and b = 3. Plugging those values into the formula, we get:
(x + 3)(x^2 - 3x + 3^2)
Simplifying further, we have:
(x + 3)(x^2 - 3x + 9)
So, the factored form of x^3 + 27 is (x + 3)(x^2 - 3x + 9).