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put this solution on YOUR website!Hi, Hope I can help,
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Not sure if this is the right section but will someone please help.
Find the LCM of
and
Thanks
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First, we can see if the two "numbers" can be factored
.
To find factors of something, you have to put the "m's" in paretheses ( since "
=
,
.
For
, (m )(m ) , next we have to find all factors of (-5), and the factors have to add up to (-4), the middle term
.
Factors of (-5), (-5) and (1), (-1) and (5), now add each pair of factors
.
,
.
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The first pair of factors add up to (-4), our middle term
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We can put (-5) and (1) in our paretheses
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(m )(m ) = (m - 5)(m + 1), if we used the FOIL method we would come up with our original equation
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(m - 5)(m + 1) =
=
=
=
.
(Remember the negative and positive signs,
=
(Our answers are true)
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The factors for our first "number" = (m - 5)(m + 1)
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Now we will find the factors of the second equation,
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First, we put the "m's" in parentheses, (m )(m )
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Remember, the factors of "7" add up to the middle term "8"
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Factors of "7", (-7) and (-1), (1) and (7)
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Adding them we get,
.
.
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The second factors work. We can put the factors in the parentheses
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(m + 1)(m + 7), If we used the FOIL method,
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(m + 1)(m + 7) =
=
=
=
.
Remember signs,
=
( our factors our true )
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Our factors for our second "number" = (m + 1)(m + 7)
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We can now put the factored equations side by side
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Equation (1), (m - 5)(m + 1)
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Equation (2), (m + 1)(m + 7)
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To find the LCM, we count all the DIFFERENT factors
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All factors put together = (m - 5)(m + 1)(m + 1)(m + 7),
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There are three different factors, (m - 5)(m + 1)(m + 7), ( both numbers have (m + 1) in common, so we only count that factor once )
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The LCM would then be
, if we expanded it,
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The LCM =
.
Hope I helped, Levi
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