How do you factor #4b^3 +3b^2-16b-12#?

2 Answers
Alan P.
May 5, 2015

Regroup to maximize the extractable factors
#4b^3+3b^2-16-12 = color(red)(4b^3-16b) + color(blue)(3b^2-12)#

#=color(red)(4b(b^2-4)) + color(blue)(3(b^2-4))#

#=(4b+3)(b^2-4)#

Recognize the second term as the Difference of Squares
#=(4b+3)(b+2)(b-2)#

Gió
May 5, 2015

Collect #4b# between the first and third term and #+3# between the second and rourth:
#4b(b^2-4)+3(b^2-4)=# collect #(b^2-4)#
#(b^2-4)(4b+3)#

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