Use the Factor Theorem to determine a polynomial equation, of lowest degree, that has only the indicated roots: 0 is a root of multiplicity 5, 2 is a double root

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Use the Factor Theorem to determine a polynomial equation, of lowest degree, that has only the indicated roots: 0 is a root of multiplicity 5, 2 is a double root

Mathematics
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x^5(x-2)^2=0
ok i cant read. start with \[x^5(x-2)^2\] and multiply out
so I would get \[x ^{5}+x ^{2}-4x+4\]

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Other answers:

no i don't think so
\[x^5(x-2)^2=x^5(x-2)(x-2)=...\]
where does the extra (x-2)^2 come from then that you have after the x^5?
oh nvm.... so what am I multiplying out then? the (x-2)^2 or?
\[x^5(x-)(x-2)=x^5(x^2-4x+4)=x^7-4x^6+4x^5\]
Oh ok so I just needed to continue multiplying to completly get rid of the parenthisis cool thank you... so what if it is the same question but it says 1/3 is a double root and -2 is a double root? do I set it up like this: f(x)=(x-1/3)^2(x+2)^2
Yes
awesome thanks so much for the help!
yw
Uh so I actually have one more silly question how do I get rid of the fraction to make that problem easier?
NVM I figured it out:) thanks
i wouldn't
oh looks like you got it right? start with \((3x-1)^2\)
Thanks:)

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