1. ## functions

I missed a day and got more behind than I expected. He tried to reexplain the lesson to me when I went back, but it wasn't as clear as I wanted to hear it. Just wondering if you guys can lend me a hand:

I want to know how to determine all of the real zeros in these two equations by factoring them:

A.) g(x)= -3x^3+11x^2-15x+2
B.) f(x)= 100x^3-403x^2+406x+1

And in these few, I'm not even sure what to do. I'm not sure if I'm solving for something, graphing it to find something or simply writing out an equation to fit its standards:

"In these, find a polynomial with real coefficients satisfying the given conditions."

A.) Degree 2; 2 as only real zero.
B.) Degree 3; -2, 1 and 4 as zeros.
C.) Degree 3; -1 as only real zero.

If f(x)=2x^3-3kx^2+kx-1, find a number k so that the graph of f contains the point (1,9).

Determine a linear factor of f(x)=(x-1)^6-64

Alright, that's all. You can reply to anything. I'm going to appreciate all, if any, responses. Thanks a whole lot.

-Amanda

2. Originally Posted by amandarporter
I missed a day and got more behind than I expected. He tried to reexplain the lesson to me when I went back, but it wasn't as clear as I wanted to hear it. Just wondering if you guys can lend me a hand:

I want to know how to determine all of the real zeros in these two equations by factoring them:

A.) g(x)= -3x^3+11x^2-15x+2
B.) f(x)= 100x^3-403x^2+406x+1

And in these few, I'm not even sure what to do. I'm not sure if I'm solving for something, graphing it to find something or simply writing out an equation to fit its standards:

"In these, find a polynomial with real coefficients satisfying the given conditions."

A.) Degree 2; 2 as only real zero.
B.) Degree 3; -2, 1 and 4 as zeros.
C.) Degree 3; -1 as only real zero.

If f(x)=2x^3-3kx^2+kx-1, find a number k so that the graph of f contains the point (1,9).

Determine a linear factor of f(x)=(x-1)^6-64

Alright, that's all. You can reply to anything. I'm going to appreciate all, if any, responses. Thanks a whole lot.

-Amanda
Im too lazy to do the first one...Ill let someone else take that
f
But for the second one you need to find k such that

$9=2-3k+k-1$

For the third we can see that

$(x-1)^6-64=\left((x-1)^3+8\right)\cdot\left((x-1)^3-8\right)$

$=(x+7)\left((x-1)^2-8(x-1)+64\right)\cdot(x-9)\left((x-1)^2+8(x-1)+64\right)$

There are two linear factors there

3. Thanks a lot. I wouldn't have figured that on my own.

4. Originally Posted by amandarporter
Thanks a lot. I wouldn't have figured that on my own.
Anytime!