SOLUTION: Find all values of k so that each trinomial can be factored as two binomials using integers: 2x^2 + 12x + k,k > 0 THANK YOU FOR ANY HELP!

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Question 297127: Find all values of k so that each trinomial can be factored as two binomials using integers:
2x^2 + 12x + k,k > 0
THANK YOU FOR ANY HELP!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find all values of k so that each trinomial can be factored as two binomials using integers:
2x^2 + 12x + k, k > 0
:
Pick two even integers whose sum is 12
10 and 2
Divide 10 by 2 = 5
two factors
(2x + 2)(x + 5) = 0
FOIL
2x^2 + 10x + 2x + 10 = 0
2x^2 + 12x + 10 = 0
k = 10
:
Do the same with 8, 4
factor
(2x+4)(x + 4) = 0
2x^2 + 8x + 4x + 16 = 0
2x^2 + 12x + 16 = 0
k = 16
:
do the same with 6, 6
(2x+6)(x+3) = 0
2x^2 + 6x + 6x + 18 = 0
2x^2 + 12x + 18 = 0
k = 18