SOLUTION: Please help me factor and check this trionomial: 2x^2+7x+3=

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Question 45127: Please help me factor and check this trionomial: 2x^2+7x+3=

Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2%2B7x%2B3=%28ax%2Bb%29%28cx%2Bd%29
looking at the coefficient of x%5E2 on the left hand side of the equation:
2x%5E2=%28ax%29%28bx%29
2x%5E2=abx%5E2
So ac=2........................(1)
Now look at the cofactors of x:
7x=adx%2Bbcx
So 7=ad%2Bbc......................(2)
Now look at the constant terms:
3=bd..............................(3)
Looking at equation (1), since thwe number 2 is a prime number, there are only two numbers that "a" and "c" could be: 1 and 2.
Let a=2 and c=1.
Looking at equation (3), since thwe number 3 is a prime number, there are only two numbers that "b" and "d" could be: 1 and 3. This time we need to make sure that we get these two numbers the right way round, so we check with equation (2):
7=2d%2Bb
so if b and d can omly be 1 or 2, the only the above equation works is if b=1 and d=3.
Put the values of a, b, c and d into the equation at the very top:
2x%5E2%2B7x%2B3=%282x%2B1%29%28x%2B3%29
I hope this helps.
Adam
P.S. please visit my website, I only set it up lastnight and it may be of use to you. The address is htttp://geocities.com/quibowibbler