SOLUTION: How do I factor 16t^2 -180+464?

Question 22014: How do I factor 16t^2 -180+464?
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
16t^2 -180+464?..TAKE OUT COMMON FACTOR IF ANY FIRST..HERE 4 IS COMMON...SO..
=4(4T^2-45T+116)...NOW TAKE THE PRODUCT OF T^2 AND CONSTANT TERMS=4*116=464..TRY TO FIND 2 FACTORS FOR THIS PRODUCT WHOSE SUM IS THE COEFFICIENT OF X TERM =-45...WE HAVE (-16)*(-29)=+464 AND -16-29=-45...SO NOW REWRITE THE GIVEN EXPRESSION BREAKING MIDDLE TERM OF -45T AS -16T-29T AND TAKE OUT COMMON FACTORS..
=4(4T^2-16T-29T+116)
=4{4T(T-4)-29(T-4)}
=4(T-4)(4T-29)
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