Question 291699
Look for a solution that looks like,
{{{(2p-a)(p-b)=2p^2-9p+10}}}
If we work out the left hand side using FOIL,
{{{2p^2-2bp-ap+ab=2p^2-9p+10}}}
{{{2p^2-(2b+a)p+ab=2p^2-9p+10}}}
Compare coefficients of {{{p^2}}}, {{{p}}} and the constant. 
{{{2p^2=2p^2}}} No information.
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{{{-(2b+a)p=-9p}}} 
{{{2b+a=9}}}
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{{{ab=10}}}
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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+a=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(2)+5=4+5=9}}}
That's the pair. 
{{{(2p-a)(p-b)=2p^2-9p+10}}}
{{{(2p-5)(p-2)=2p^2-9p+10}}}