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?

Question

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?

myininaya · Answer

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.

anonymous · Answer

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.

myininaya · Answer

Do you know synthetic division?

anonymous · Answer

We haven't learned that yet

myininaya · Answer

Do you know long division then?

anonymous · Answer

yes

myininaya · Answer

Great. Since x=2 is a zero, then x-2 is a factor of 3x^3-8x^2-x+9+1

myininaya · Answer

See what another factor is by seeing how many times x-2 goes into 3x^3-8x^2-x+10

myininaya · Answer

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.

anonymous · Answer

Thank you, I will try that!