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Simplify Using long division

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1 Answer

          ______________
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