Divide using long division. (-2x^3-4x^2-4x+2)/(x-4) (MULTIPLE CHOICE)

Question

Divide using long division.  (-2x³-4x²-4x+2)/(x-4)    

Answer 1

 

            -2x² -12x -52

          _________________

(x-4) / -2x³ - 4x² - 4x + 2

          -(-2x³ +8x²)

          ------------------------

                  -12x² - 4x + 2

               -(-12x² +48x)

                --------------------

                           -52x + 2

                         -(-52x+208)

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

                                 -206   This is the remainder.

 

(-2x³ -4x²-4x+2)/(x-4)= -2x²-12x-52 -206/(x-4)

 

with the long division, each time you multiply the (x-4) by whatever will make the first term of the product equal to the highest term in the polynomial you are dividing it into. Do the multiplication and subtract the result.

 

That is why for the first term we multiplied (x-4) by -2x² in order to make the first term of that product equal to -2x³ so that when we subtracted the first term would be eliminated.

 

Do the same for each sum until the resulting sum has a lower power than that of (x-4).    Note that x-4 has an order of 1 because the highest exponent is x¹.  thus we go until the sum is down to x⁰ ... which means until the sum is just a constant with no x variable left.