Rational equations, please help.?

Question

1. Solve the rational equation below.
(z^2)/(8) - (7z)/(8) = 1

2. Solve the rational equation below.
(n^2)/(2)-(5n)/(6) -2 =0

3. Solve the rational equation below.
(x+1)/(2x)=(x-1)/(2x-1)

4. Find one ordered pair solution for the equation below, when x=2.

f(x)=2x3+x2-10x-5

(2,3)
(2,-3)
(2,5)
(2,-5)

5. Find the remainder when x3-5x2+8 is divided by x-2.

Note: You must make adjustments for the missing x-term.
0
-4
-20
-32

6. Is (x-3) a factor of p(x)=x4-5x2-27x+15?

7. Find the zeros of the polynomial:

f(x) =(x-4)(x+2)(x-1)

8. For the polynomial P(x)= 2x3+5x2-3x-4

a. Use Descartes' Rule to analyze the zeros of the function.
b. Use the Rational Zeros Theorem to identify the possible rational zeros.

9. Given a zero: x=2, of the polynomial: x3-4x2+21x-34=0, find the others.

Thanks for helping guys, algebra is really my worst subject and i cant figure out how to do these.

Answer 1

1. (z^2)/(8) - (7z)/(8) = 1
z^2 - 7z = 8
z^2 - 7z - 8 = 0
(z + 1)(z - 8) = 0
z = 8 or -1

Good luck!

Answer 2

... 10/(x-1) + 1 = 20/(x²-1) ... x ≠ ±1 ← Else equation becomes undefined or 10/(x-1) + 1 = 20/[ (x-1)(x+1) ] or 10(x+1) + (x-1)(x+1) = 20 or 10x + 10 + x² - 1 = 20 or x² + 10x - 11 = 0 or (x - 1) (x + 11) = 0 or x = 1 ....... ← Reject due to initial constraint or x = -11 .... ← Final solution

Answer 3

2.
(n^2)/(2) - (5n)/(6) - 2 =0
n^2 - (5/3)n = 4
n^2 - (5/3)n + 25/36 = 4 + 25/36
(n - 5/6)^2 = 169/36
n - 5/6 = ± 13/6
n = -4/3, 3

Your turn now!

Answer 4

1) x1 = 8 , x2 = -1

2) x1 = 3 , x2 = -4/3

3) x = 1/3

4) (2,-5)

5) -6x+8

6) NO

7) x = 4 , x = -2 , x = 1

8) DNK

9) DNK

Answer 5

(n^2)/(2)-(5n)/(6) -2 =0
2*((n^2/(2)-(5n)/(6)-2)=0*2
(n^2)-(5n)/(3)-4=0
3*((n^2)-(5n)/(3)-4)=0*3
(3n^2)-(5n)-12=0
(3n+4)(n-3)=0
n-3=0
n=3
and
3n+4=0
3n=-4
n=-4/3