SOLUTION: Factor by grouping. 6x^3 + 21x^2 – 2x – 7 I came up with (2x+7)(3x^2-1) I hope that someone can tell me if this is correct???? Thank you.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor by grouping. 6x^3 + 21x^2 – 2x – 7 I came up with (2x+7)(3x^2-1) I hope that someone can tell me if this is correct???? Thank you.      Log On


   

Question 69626: Factor by grouping. 6x^3 + 21x^2 – 2x – 7
I came up with (2x+7)(3x^2-1)
I hope that someone can tell me if this is correct???? Thank you.
Found 2 solutions by checkley75, bucky:
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
6X^3+21X^2-2X-7
(6X^3-2X)+(21X^2-7)
2X(3X^2-1)+7(3X^2-1)
(2X+7)(3X^2-1)
YOU ARE CORRECT!!!!!!

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Let's check your answer by multiplying your factors together using the FOIL method (first terms, outside terms, inside terms, and last terms)
Your answer was:
%282x%2B7%29%2A%283x%5E2-1%29
Multiplying the first terms in each factor results in:
2x+%2A+3x%5E2+=+%2B6x%5E3
Multiplying the outside terms in each factor results in:
2x%2A%28-1%29+=+-2x
Multiplying the inside terms in each factor results in:
7%2A3x%5E2+=+%2B21x%5E2
And finally, multiplying the last terms in each factor:
7%2A%28-1%29+=+-7
Algebraically adding all these terms in descending powers of x results in:
6x%5E3+%2B+21x%5E2+-+2x+-+7
That is exactly the expression you started with. So your answer is correct. Excellent job. Keep up the good work!