How do you factor #3t^3+2t^2-48t-32#?

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Answer 1 · 2017-05-19T04:26:13

Use group factoring and difference of squares: #(3t+2)(t-4)(t+4)#

Given: #3t^3 + 2t^2 - 48t - 32#

Use group factoring by factoring the GCF from the two groups:

#3t^3 + 2t^2 - 48t - 32 = (3t^3 + 2t^2) - (48t + 32)#

# = t^2(3t + 2) - 16(3t + 2)#

Notice that both groups have the factor #(3t+2)#. Factor this from each group:

# =(3t + 2) (t^2 - 16)#

Realize that #t^2 - 16 = t^2 - 4^2# is the difference of squares.

Difference of squares #a^2 - b^2 = (a + b) (a - b)#

#3t^3 + 2t^2 - 48t - 32 = (3t + 2) (t - 4)(t + 4)#