Divide the following: (x2-16x+49) ÷ (x-8)

Question

 Trying to do an online math quiz and wondering if anyone would be willing to help me out?

Answer 1

There are a couple ways to do this problem: long division and synthetic division. Just in case you haven't run into synthetic division yet, here's the long division method:

 

          x - 8 - ¹⁵/_(x-8)

        ______________

x-8 | x² - 16x + 49

      - (x² - 8x)

      ---------------

                 -8x + 49

               - (8x + 64)

                 ----------------

                            -15

 

In order to make it x², x must be multiplied by x. Just like in normal long division, multiply the divisor (x-8) by x and subtract (from x² - 16x). Then bring down the next term (49).

 

Next, in order to make it 8x, x must be multiplied by -8. Again, multiply the divisor (x-8) by -8 and subtract. There are no more terms to bring down, so your remainder is -15.

 

Make the remainder the numerator in a fraction with the divisor as the denominator (-15/(x-8)). Add this to the expression at the top (x - 8).

 

Your answer is:

 

x - 8 - ¹⁵/_(x-8)

 

 

Check your work by multiplying the answer by x - 8:

 

(x - 8)(x - 8 - 15/(x-8))

x(x-8) - 8(x-8) - (15(x-8)/(x-8))

x² - 8x - 8x + 64 - 15

x² - 16x + 49