sabika13
Prove that (xa) is a factor of x^3  (a + b + c)x^2 + (ab +bc + ca)xabc. How do I prove this???



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anonymous
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show that if you replace \(x\) by \(a\) you get 0

anonymous
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then you know if \(a\) is a root of a polynomial \(p(x)\) then you can factor as \(p(x)=(xa)(q(x))\)

sabika13
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yeah i tried that, but i couldnt end up with a zero..

anonymous
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if you do not get 0, then you cannot factor

sabika13
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i probably made a mistake.. because it has to equal to zero

anonymous
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\[a^3  (a + b + c)a^2 + (ab +bc + ca)aabc\] is a startr

anonymous
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yeah it works, try again

sabika13
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a^3  (a + b +c)a^2 + (ab+ bc +ca)a abc
= a^3  a^3 + a^3b + a^3 c + a^2b + bc+ca^  abc

sabika13
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ohhh i see it, i messed up

anonymous
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hmmm forgot the distributive property for the second term

anonymous
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and some other mistakes too, but you can clean it up i am sure

sabika13
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okay i tried and i ended up like this: 2a^2 + 2a^2c

anonymous
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lets go slow

sabika13
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ohh its negative.. i got it

anonymous
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first step
\[a^3  (a + b + c)a^2 + (ab +bc + ca)aabc\] second step
ok

sabika13
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yeah i didnt see the negative sign infront of the first bracket, thank you so much!!

anonymous
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yw (you did all the work)