1. ## Pre-Calc Questions

I'm having a hard time with some problems and can't seem to come up with anything that will work. I have a pre-calc final 2 hours, please help!

1. Perform the following operations and reduce to simpliest form: --My answers didn't work out
a) [x^2-4)/(x^4-2x^2-8][(x^2+2)/x^2]
b) [x-1]+[1/(x+2)]+[1/(x-1)]

2. Find all rational zeros using the rational zero test: --Can't remember how to do the rational zero test...
F(x)=x^4-8x^3+17x^2-8^x+16

3. Write the equation of a line that is parallel to 2x+3y=6, that passes through the point (1,-1)

4. The vertices of a triangle are located at (1,-1), (1,3), and (4,2). Write the equation for the sides of the triiangle. --Do I use slope and distance or something else?

2. Hi

2. $\displaystyle F(x)=x^4-8x^3+17x^2-8x+16$
Let $\displaystyle \frac{p}{q}$ a rational zero of F, p and q having no common factor

$\displaystyle \left(\frac{p}{q}\right)^4-8\left(\frac{p}{q}\right)^3+17\left(\frac{p}{q}\ri ght)^2-8\left(\frac{p}{q}\right)+16 = 0$

Multiplying by $\displaystyle q^4$

$\displaystyle p^4-8p^3q+17p^2q^2-8pq^3+16q^4=0$

p divides 0 therefore p divides $\displaystyle p^4-8p^3q+17p^2q^2-8pq^3+16q^4$

And p divides each item of the sum therefore p divides $\displaystyle 16q^4$
p and q having no common factor p divides 16
p = +/- 1, 2, 4, 8, 16

Same method for q leads to q=1

3. All the parallels to 2x+3y=6 have an equation like 2x+3y=c
The one passing through the point (1,-1) is therefore 2x+3y=2.1+3.(-1)=-1

3. Thanks running-gag for 2 and 3. Also with 1 and 4 I have another question this ones long but I just need to know a way to go at it.

5. A veterinarian wants to control the diet of an animal so that on a monthly basis the animal consumes 60 pounds of oats, 75 pounds of corn, and 55 pounds of soybeans. There are three feeds available. How many pounds of each feed should be used to obtain the desired mix?

1lb. of feed a
oats-6oz
corn-5oz
soybeans-5oz

1lb. of feed b
oats-6oz
corn-6oz
soybeans-4oz

1lb. of feed c
oats-4oz
corn-7oz
soybeans-5oz

I've tried setting up equations like for feed a
16oz=6x+5y+5z

But all I found out was that x=y=z and they all equal 1.

4. I am not used to such volume units !
I found on the web that 1 pound = 16 oz right ?

Therefore the quantity of oats is 6x + 6y + 4z = 60 x 16 = 960
Do the same for corn and soybeans and you will get a linear system

5. Originally Posted by running-gag
Therefore the quantity of oats is 6x + 6y + 4z = 60 x 16 = 960
Do the same for corn and soybeans and you will get a linear system
Yeah 1lb=16oz

Sorry but I'm not the best at math....with that equation how did you get the 60?

6. x is the quantity of feed a, y of feed b and z of feed c
The quantity of oats (in oz) is 6x + 6y + 4z
The veterinarian wants the animal to consume 60 pounds (960 oz) of oats
Therefore 6x + 6y + 4z = 960

7. Oh....thanks

8. Ok I got all of the values....x=30 y=70 and z=90 but How do I know how many pounds of each feed should be used?

9. You have to divide all these figures by 16 (what an amazing system of units ! )