How do you factor #8x^3+28x^2+24x #?

1 Answer
George C.
May 10, 2015

#8x^3+28x^2+24x = 4x(2x^2+7x+6) = 4x(2x+3)(x+2)#.

To find this, first note that all the terms are divisible by #4# and by #x#. Dividing through by #4x# yields the quadratic #2x^2+7x+6#.

If this has linear factors with integer coefficients they must be of the form #(2x+a)# and #(x+b)# in order that the product starts with #2x^2#, where #ab=6# and #2b+a=7#. From this, it's easy to see that #a=3# and #b=2#, so #2x^2+7x+6 = (2x+3)(x+2)#.

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