Question

X^3-8/x-2 simplify and I need an explanation please

Answer 1

Answer: $x^2+2x+4$

Step-by-step explanation:

The expression given in the exercise is:

 $\frac{x^3-8}{x-2}$

If you descompose the number 8 into its prime factors, you get that:

$8=2*2*2=2^3$

Therefore, you can rewrite the numerator of the expression as following:

$=\frac{(x^3-2^3)}{(x-2)}$

For this exercise you need to remember that for a  Difference of cubes:

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

Then, applying this, you get:

$=\frac{(x-2)(x^2+2x+2^2)}{(x-2)}=\frac{(x-2)(x^2+2x+4)}{(x-2)}$

Now, it is necessary to remember the following:

$\frac{a}{a}=1$

Knowing the above, you can say that:

$\frac{(x-2)}{(x-2)}=1$

Therefore applying this, you get that the simplified expression is:

$=x^2+2x+4$