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Question

Factor the quadratic expression m2-9m+8 completely.


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Solution

Factor the quadratic polynomial m2-9m+8.

Find the product of the quadratic term m2 and the constant term 8, m2×8=8m2 . Through a hit and trial process, we have to find two factors of 8m2 that add up to give the linear term -9m. The two factors that satisfy these conditions are -8m and -m, because their sum is equal to the linear term -9m and their product is equal to 8m2.

Rewrite the term -9m in the expression m2-9m+8 as -8m-m.

Then factorize by grouping the terms:

m2-9m+8=m2-8m-m+8=m-8m+-m+8=mm-8-1m-8=m-8m-1

Thus, m2-9m+8 is completely factorized to obtain (m-8)(m-1).


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