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The function f(x)= kx^3 - 8x^2 -x + 3k + 1 has a zero when x=2. Determine the value of k. Graph f(x) and determine all the zeros. Then rewrite in factored form. I found that k=3 so far, but I'm not sure how to graph it without making a table of values, or how to find the zeros. Any ideas?

Mathematics
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So f is 0 when x=2 So write this f(2)=0 except actually evaluate the function given at x=2 Replace all of those x's with 2 and then set that result to 0.
I did that already to find the k value (3), but I'm stuck on the graphing part. And also on how to find the zeros.
Do you know synthetic division?

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Other answers:

We haven't learned that yet
Do you know long division then?
yes
Great. Since x=2 is a zero, then x-2 is a factor of 3x^3-8x^2-x+9+1
See what another factor is by seeing how many times x-2 goes into 3x^3-8x^2-x+10
I must leave but you should get a quotient and no remainder. You should be able to factor the quotient. You should be able to now find your 3 zeros. Test the intervals between and before and after each zero to see if the function is above or below the x-axis. Then connect the dots.
Thank you, I will try that!

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