How do you find the quotient of #(x^2+3x-28)div(x+7)#?

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Answer 1 · 2017-02-09T13:19:31

See the entire solution process below:

First, rewrite the problem as:

#(x^2 + 3x - 28)/(x + 7)#

Next, factor the numerator:

#((x + 7)(x - 4))/(x + 7)#

Then, cancel the common terms in the numerator and denominator:

#(color(red)(cancel(color(black)((x + 7))))(x - 4))/(color(red)(cancel(color(black)((x + 7))))#

#x - 4#

However, because you cannot divide by #0# we must qualify this answer:

#(x^2 + 3x - 28) -: (x + 7) = (x - 4)# where #x != -7#