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rach_ell
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?
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?
We haven't learned that yet
Do you know long division then?
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!