
Had Make up test
So basically I had a make up test in PreCalc and right now I feel like ripping my hairs out for I have no idea if I got certain questions right. Any help will be appreciated. Thanks in advance
From the top of my head I remembered certain questions such as:
1) You have 2x^4+3x^3+7x^27x5
I had to find the root now was I supposed to use the basic p over q and plug in which were correct roots?
2)This one killed me
4x^4+8x^3+7x*5
I had to find the smallest root?
3) This one also confused me and I could not answer. It gave me two roots 2+i and 3. I was supposed to find out the cubic polynomial. How exactly is this done?
Thanks in advance for anyone who is willing to help.

Reply
Root for the first polynomial are gonna be
$\displaystyle
\frac {factors of 5}{root factors of 2} = \pm \frac{1}{2} \pm 1 \pm \frac{5}{2} \pm 5
$
In this case $\displaystyle
1 and \frac{1}{2}
$
Solve number 2 and 3 with the same technique.
Once a root works, use the division to get the next polynomial.

If a root is 2+i, then another root is 2i, assuming that the polynomial has real coefficients. Then you have 3 roots, multiply the corresponding polynomials, such as (x3), and you have your cubic polynomial.