How do you completely factor #6x^3+7x^2-1# given #2x+1# is one of the factors?

1 Answer
Narad T.
Oct 22, 2016

The complete factorization is #(2x+1)(3x-1)(x+1)#

Explanation:

We have to make long division

#6x^3+7x^2# #color(white)(aaaa)# # -1# #color(white)(aaaaaa)# #∣2x+1#
#6x^3+3x^2# #color(white)(aaaaaaaaaaaaaa)# # 3x^2+ 2x-1#
#0 +4x^2 +2x#
#color(white)(aaaaaaa)# #-2x-1#
#color(white)(aaaaaaaa)# #+0 -0#

So the result of the long division is #3x^2+2x-1#

which upon factorization gives #(3x-1)(x+1)#

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