Factor 4m2 – 16m + 15 completely.
1 answer:
Answer:
(2m -3)(2m -5)
Step-by-step explanation:
You can do this several ways. One of my favorites is to graph the expression to find its zeros. They are 3/2 and 5/2, so the factoring can be ...
... 4(x -3/2)(x -5/2) = (2x -3)(2x -5) . . . . . . after eliminating fractions
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You can also look for factors of 4·15 ("ac") that add to give -16 ("b"). Since "b" is negative, both factors will be negative.
... 4·15 = 60 = (-1)(-60) = (-2)(-30) = (-3)(-20) = (-4)(-15) = (-5)(-12) = (-6)(-10)
The pair -6, -10 has a sum of -16, so we can rewrite the expression as ...
... 4m^2 -6m -10m +15 . . . . . . . replace -16m with -6m -10m (order doesn't matter)
and factor pairs of terms
... (4m^2 -6m) -(10m -15) = 2m(2m -3) -5(2m -3) . . . . . there is a common factor between the pairs
... = (2m -5)(2m -3)
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