Simplify Using long division

Question

(w³ - 15w - 11) ÷ (w-4)

Answer 1

          ______________

w - 4 / w³ - 15w - 11              

 

first check your polynomial to see if it contains all powers of the variable w. If not, you must add placeholders for them using zero as the coefficient. In this case, the second power is missing so we add 0w²

 

         ___________________

w - 4 /w³ + 0w² - 15w - 11         now we are ready to divide

                                                  

the first step is w³ ÷ w (first term divided by first term) and you put the answer on top. Then you multiply your answer by the divisor (w - 4) and write the answer below the dividend. Then you substract. Then you bring down the next term and add it to the new dividend. The second step is the same as the first only now you use the new dividend and divide the first term by first term.   This is what it looks like.

 

         ______w² + 4w + 1
w - 4 /w³ + 0w² - 15w - 11      

          w³ - 4w²

                 4w² - 15w

                 4w² - 16w

                             w - 11

                             w - 4

                                    -7

 

So the answer is w² + 4w + 1    with remainder   -7   or we write   -7 / w - 4

 

To check your answer you multiply (w - 4) (w² + 4w + 1 -7/(w - 4) ) and you should get the original dividend