How do you find the quotient of #(t^2+5t+4)div(t+4)#?

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Answer 1 · 2017-02-21T13:55:19

First, rewrite this expression as:

#(t^2 + 5t + 4)/(t + 4)#

Next, factor the numerator:

#((t + 4)(t + 1))/(t + 4)#

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

#(color(red)(cancel(color(black)((t + 4))))(t + 1))/(color(red)(cancel(color(black)(t + 4))# #= t + 1# where #t + 4 != 0# or #t != -4#

Answer 2 · 2017-02-21T13:56:13

You can factorize #t^2+5t+4=(t+1)(t+4)#

So now we have:
#=((t+1)(t+4))/(t+4)#

We may now cancel the #(t+4)#'s provided #t!=-4#

#=((t+1)cancel((t+4)))/cancel(t+4)=t+1#