SOLUTION: Factor completely. If a polynomial is prime, state this. 6x^2 + 19x + 10

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Question 474207: Factor completely. If a polynomial is prime, state this.
6x^2 + 19x + 10
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
6x^2 + 19x + 10
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6x^2+4x+15x+10
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2x(3x+2)+5(3x+2)
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= (3x+2)(2x+5)
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Cheers,
Stan H.
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Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


You can, if such nonsense appeals to you, muck about with trial and error trying to find sets of factors of 6 and 10 so that the middle term comes out to be 19. But there is a much easier way.

Set the trinomial equal to zero and then solve using the quadratic formula (alternatively, use one of the many on-line quadratic solvers).





If you get to this point and you have a radicand that is not a perfect square, you can just say that the trinomial is prime and quit here. Your example is the opposite situation, so continue:



.

So if then

Likewise, if then

And there you have your two factors.

John

My calculator said it, I believe it, that settles it
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