mscrosscountry
Select one of the factors of 3x2 + 10x + 3



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mscrosscountry
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thats not one of my options though. (3x + 1)
(3x + 3)
(3x – 1)
None of the above

myininaya
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\[3x^2+9x+x+3\]
I just found two factors of 3(3) that added up to be 10
Factor this by grouping

myininaya
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What factors does 3x^2 and 9x have in common?

mscrosscountry
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the factors they have in common is 3

myininaya
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and x right?

myininaya
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\[3x(x+3)+1(x+3)\]
Now we have two terms.
What do these two terms have in common?

mscrosscountry
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so the answer is none of the above because its not one of my options

myininaya
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we aren't done

myininaya
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I was just asking you what 3x^2 and 9x had in common so that we can factor this beast

mscrosscountry
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both have 3x in common?

myininaya
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right so from the first two terms i factored out 3x
giving me
\[3x(x+3)+x+3\]

myininaya
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But we can write this as
\[3x(x+3)+1(x+3)\]
since 1(x+3) is still x+3

myininaya
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now what factors does 3x(x+3) and 1(x+3) have in common besides the factor 1?

mscrosscountry
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3x again?

myininaya
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no they both have the factor (x+3) in common

myininaya
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\[(x+3)(3x+1)\]

mscrosscountry
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so the answer is (3x + 1)

myininaya
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x+3 and 3x+1 are both factors of the polynomial given

Sdowney
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x+3 & 3x+1 are the factors