SOLUTION: Factor... 3x2 � 11x + 10 8x3 + 1 with those two i just cannot get the right answer... :-(

Question 181905: Factor...
3x2 � 11x + 10

8x3 + 1
with those two i just cannot get the right answer... :-(
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
3x2 � 11x + 10
= (3x-5)(x-2)
.
.
8x^3 + 1
Notice this is "sum of cubes":
(2x)^3 + (1)^3
Sum of cubes, fall under a "special" factoring class. You are expected to remember:
A^3 + B^3 = (A + B)(A^2 - AB + B^2)
Therefore:
(2x)^3 + (1)^3
So, in your case:
A=2x and B=1
(A + B)(A^2 - AB + B^2)
(2x + 1)((2x)^2 - (2x)(1) + (1)^2)
(2x + 1)(4x^2 - 2x + 1)
.
So:
8x^3 + 1 = (2x + 1)(4x^2 - 2x + 1)

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