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

Question

I want to know how to solve and check my answer

Answer 1

One method is "long division" . Using this method, you compare the leading terms of your numerator and denominator. 

How many times does x (from x + 2) go into 4x³ ? 4x² times (x * 4x² = 4x³). So we also multiply the 2 (from x + 2) by 4x² (to get 8x²), and now we subtract it from our numerator, and we are left with (-x-2)/(x + 2)

Now, how many times does x go into -x ? -1 times. Multiply and subtract:

-x - 2 - (-1)(x + 2) = 0 

So our result is 4x² - 1

__4x² ______   -1  _________________

x + 2      | 4x³ + 8x² - x - 2

4x³ + 8x²
---------------------

-x - 2
-x - 2

--------

      0

 

 

Answer 2

A way to check your answer, which is correct from Kevin S., is to multiply both the numerator and denominator by the original denominator (x+2).  As shown:

(4x^2 - 1) / 1 * (x + 2) / (x + 2)  (doing this step is effectively multiplying your answer by "1")

(4x^2 - 1)*(x + 2) / (x+2)

(4x^3 + 8x^2 - x - 2) / (x + 2)  (FOIL)

Since we got the same answer, the solution checks out.