Question

What is the result of dividing x3−6 by x + 2?

Answer 1

Answer:    $\bold{x^2-2x+4-\dfrac{14}{x+2}}$

Step-by-step explanation:

I am going to use Synthetic Division.

The divisor is:    x + 2 = 0     →   x = -2

The coefficients are: 1x³ + 0x² + 0x - 6    →      1, 0, 0, -6

-2 |  1      0     0     -6

   |  ↓     -2     4     -8          

      1     -2      4    -14    ← remainder

Reduced Polynomial is: x² -2x + 4 -  14/(x + 2)

Answer 2

The result of dividing x³ - 6 by x + 2 gives;

(x + 2)(x² -  2x  + 4) - 14

• We are given the functions;

f(x) = x³ - 6

g(x) = x + 2

We want to divide x³ - 6 by x + 2. This denotes f(x)/g(x)

• This is simply solved by making use of long division method of polynomials.

Thus; f(x)/g(x) = (x³ - 6)/(x + 2)

            x² -  2x + 4

           ______________

  x + 2 I x³ - 6

          - (x³ + 2x²)

           ----------------  

                    -2x²  - 6  

                  -(-2x² - 4x)  

                  -------------------  

                                4x -  6  

                              -(4x + 8)  

                                -------------  

                                           -14

• We can see we have a quotient and a remainder. Thus, the final solution will be written as;

(x + 2)(x² -  2x  + 4) + (-14)

⇒ (x + 2)(x² -  2x  + 4) - 14

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