Polynomial question (1 Viewer)

AfroNerd · Feb 24, 2016

help please!!

InteGrand · Feb 24, 2016

AfroNerd said:
View attachment 32943

help please!!

$\noindent This is not a polynomial question. This question is asking us to show that the given quantity is divisible by 3 for any integer $x$. We prove this below.$

$\noindent Call the given expression $\Psi$, and note that we can simplify it as $\Psi = 6x+2(-1)^x + (-1)^x = 6x+3(-1)^x$ (using the facts that $-(-1)^{x+1} = (-1)^{x}$ and $(-1)^{x+2} = (-1)^{x}$). Now, for any integer $x$, this expression is the sum of two integers that are divisible by 3. Hence $\Psi$ is divisible by 3 for any integer $x$. Q.E.D.$

Polynomial question (1 Viewer)

AfroNerd

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InteGrand

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