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Question

Factor the quadratic expression p2-5p-14 completely.


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Solution

Factor the quadratic polynomial p2-5p-14:

Find the product of the quadratic term p2 and the constant term -14, p2×-14=-14p2 . Through a hit and trial process, we have to find two factors of -14p2 that add up to give the linear term -5p. The two factors that satisfy these conditions are -7p and 2p, because their sum is equal to the linear term -5p and their product is equal to -14p2.

Rewrite term -5p in the expression p2-5p-14 as -7p+2p.

Then factorize by grouping the terms:

p2-5p-14=p2-7p+2p-14=pp-7+2p-7=p-7p+2

Thus, p2-5p-14 is completely factorized to obtain (p-7)(p+2).


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