Can you help me solve these Pre-Calc Problems???

Question

Please explain how to do the problems too.




Divide 3x^4-7x^2+2x-10 by x-3 using long division.



Use synthetic division to find f(-6) given f(x)=7x^3+40x^2-12x+15.




Write f(x)=f(x)=x^4+x^3+3x^2+5x-10 as a product of linear factors.




Find all the asymptotes of f(x)=8x^2-9/x^2+1



Find all the asymptotes of f(x)=4x^2-2x+7/x-1




Solve for x: (e^x+e^-x)/3=4





Thanks. <><

I have this exam in the morning, and really need to know how to do this stuff. Thanks. <><

Answer 1

(e^x+e^-x)/3=4
(e^x+e^-x)=12
(e^x+e^-x)-12=0
e^2x +12e^x+1=0
Let y=e^x:
y^2 +12y +1 =0
Solve for y with quadratic formula; then take LN of both sides.