SOLUTION: Factor completely relative to the integers. If the polynomial is prime relative to the integers, enter PRIME. 24(x - 3)(6x + 7)^2 + 15(x - 3)^2(6x + 7) Please help

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor completely relative to the integers. If the polynomial is prime relative to the integers, enter PRIME. 24(x - 3)(6x + 7)^2 + 15(x - 3)^2(6x + 7) Please help      Log On


   

Question 212823: Factor completely relative to the integers. If the polynomial is prime relative to the integers, enter PRIME.

24(x - 3)(6x + 7)^2 + 15(x - 3)^2(6x + 7)
Please help
Found 2 solutions by Earlsdon, jsmallt9:
Answer by Earlsdon(6294) About Me  (Show Source):
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
24%28x+-+3%29%286x+%2B+7%29%5E2+%2B+15%28x+-+3%29%5E2%286x+%2B+7%29
When factoring, always start with the Greatest Common Factor (GCF). In this case you have a GCF (highlighted):

Factoring out the GCF we get:
3%28x+-+3%29%286x+%2B+7%29%2A%288%2A%286x%2B7%29+%2B+5%2A%28x+-+3%29%29
Now we simplify the factor on the right:
3%28x+-+3%29%286x+%2B+7%29%2A%2848x+%2B+56+%2B+5x+-15%29
3%28x+-+3%29%286x+%2B+7%29%2A%2853x+%2B+41%29
None of these factors will factor further so we are finished.