SOLUTION: Factor: 2p^2-9p+10. Please explain.

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Question 291699: Factor: 2p^2-9p+10. Please explain.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look for a solution that looks like,
%282p-a%29%28p-b%29=2p%5E2-9p%2B10
If we work out the left hand side using FOIL,
2p%5E2-2bp-ap%2Bab=2p%5E2-9p%2B10
2p%5E2-%282b%2Ba%29p%2Bab=2p%5E2-9p%2B10
Compare coefficients of p%5E2, p and the constant.
2p%5E2=2p%5E2 No information.
.
.
-%282b%2Ba%29p=-9p
2b%2Ba=9
.
.
ab=10
.
.
Now look for possible values of a and b that solve both equations.
a=10, b=1
a=5, b=2
a=2, b=5
a=1, b=10
Try those until one works.
All of them solve
ab=10
Now solve
2b%2Ba=9
Obviously a or b cannot equal 10 since the left hand side would be greater than the right hand side.
If we let b=2 and a=5 then
2%282%29%2B5=4%2B5=9
That's the pair.
%282p-a%29%28p-b%29=2p%5E2-9p%2B10
%282p-5%29%28p-2%29=2p%5E2-9p%2B10