SOLUTION: Hello out there,I need some help with some problems,The first one is,Factor.Write prime if the expression cannot be factored:x^2+x+6.The next one is,Factor.Write prime if expressio

Question 91265: Hello out there,I need some help with some problems,The first one is,Factor.Write prime if the expression cannot be factored:x^2+x+6.The next one is,Factor.Write prime if expression cannot be factored:12w^2+10w-8.The third one is,Factor.Write prime if the expression cannot be factored:6f^2+5f+2.And the last one is,Factor.Write prime if the expression cannot be factored :3a^2+9a+6.Thanks to whoever can help.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The first one is,Factor.Write prime if the expression cannot be factored:x^2+x+6.The next one is,Factor.Write prime if expression cannot be factored:12w^2+10w-8.The third one is,Factor.Write prime if the expression cannot be factored:6f^2+5f+2.And the last one is,Factor.Write prime if the expression cannot be factored :3a^2+9a+6.
:
x^2 + x + 6 is prime; no combination of factors of 6, will give you the coefficient of x
:
12w^2 + 10w - 8
:
You can see that all coefficients, 12, 10, and -8 are even, so you can factor out 2
2(6w^2 + 5w - 4); about all we can do with it
:
:
6f^2 + 5f + 2 is prime, same as the 1st one
:
:
3a^2 + 9a + 6
:
You can see that all coefficients are multiples of 3:
3(a^2 + 3a + 2)
:
And that can be factored to:
3(a+1)(a+2)
:
When doing these, check to see if any number can be extracted from the coefficients, like we just did. Then see if it can be factored, be studying
the expression. As a last resort you can use the quadratic formula to see if it has integer values as a solution. If not, it is prime
:
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