How do you factor #p^{2}-7pq+10q^{2}#?

1 Answer
George C.
Oct 22, 2016

#p^2-7pq+10q^2 = (p-5q)(p-2q)#

Explanation:

Given:

#p^2-7pq+10q^2#

Factoring a homogeneous polynomial like this one is similar to factoring a quadratic in one variable.

SInce the coefficient of the leading term is #1#, we are looking for a pair of numbers with sum #7# and product #10#.

The pair #5, 2# works, so we find:

#p^2-7pq+10q^2 = (p-5q)(p-2q)#

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