college algebra

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for the function g(x)=5x^6-3x^3+x^2-x, list the possible rational zeros of g(x) and then use synthetic division to factor g(x) completely.

***i'm confused, doesn't this problem need a constant?****

• college algebra -

sure - it just happens to be zero.
So, factor out the x and see that

g(x)=x(5x^5-3x^2+x-1)

So, now we know 0 is a root, and any other rational roots are ±1/5

So, do a division to see that there are no other rational roots than 0.

• college algebra -

thank you!

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