sjeikdom0
2021-01-08
Answered

We need to determine if $x-5$ is a factor of $2{x}^{3}-4{x}^{2}-7x-10$

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Yusuf Keller

Answered 2021-01-09
Author has **90** answers

Simply plug in $x=5$ to the equation I found $x=5$ by doing this: $(x-5)=0$ ,

$x=52(5{)}^{3}-4(4{)}^{2}-7(5)-10=0$

If this is true then$x-5$ is a factor.

They are not equal so$x-5$ is not a factor.

If this is true then

They are not equal so

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So i have to evaluate this sum:

$\frac{1-{2}^{-2}+{4}^{-2}-{5}^{-2}+{7}^{-2}-{8}^{-2}+{10}^{-2}-{11}^{-2}+\cdots}{1+{2}^{-2}-{4}^{-2}-{5}^{-2}+{7}^{-2}+{8}^{-2}-{10}^{-2}-{11}^{-2}+\cdots}$

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My current attempt : Trying to convert this into power series

$a\left(n\right)={(3n+1)}^{-2}-{(3n+2)}^{-2}\text{}\text{}\text{}\text{}\text{}\text{}b\left(n\right)={(3n+1)}^{-2}+{(3n+2)}^{-2}$

Can a(n) and b(n) be the definite integral of certain polynomial function f(x) ?

Maybe there is a better direction. Can someone give me a hint ?

So i have to evaluate this sum:

it has the form :

My current attempt : Trying to convert this into power series

Can a(n) and b(n) be the definite integral of certain polynomial function f(x) ?

Maybe there is a better direction. Can someone give me a hint ?

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