Math help, please help...correct answers gets the points!?

Question

1.) Solve the inequality and write the solution in interval notation:
/3x + 1/>10 ...(the absolute of 3x plus 1 than greater than or equal to 10)
2.) Factor the expressions 15b2 + 4b - 4 and x64 - y64..using any method
3.) Use the factor theorem to decide wheather x-5 is a factor of P(x) = x3 - 3x2 - 8x - 10
4.)Find the domain and range of f (x) = x + 2/ x..and how you would graph that..
THANK YOU...CORRECT ANSWERS= 10PTS!

Answer 1

(1) |3x + 1|>10
that means either 3x + 1>10, or 3x + 1 < -10
thus x > 3, or x < -11/3

(2) 15b^2 + 4b - 4
= (5b - 2)(3b + 2)
by simple try-and-error.
x^64 - y^64
= (x^32 + y^32)(x^32 - y^32)
= (x^32 + y^32)(x^16 + y^16)(x^16 - y^16)
= (x^32 + y^32)(x^16 + y^16)(x^8 + y^8)(x^4 + y^4)(x^2 + y^2)(x + y)(x - y)
So far I factorized in integer domain, but it can be further factorized in real. For example:
x^4 + y^4 =
= (x^4 + 2x^2*y^2 + y^4) - 2x^2*y^2
= (x^2 + y^2)^2 - [sqrt(2)xy]^2
= (x^2 - sqrt(2)xy + y^2)(x^2 + sqrt(2)xy + y^2)

(3) P(x) = x^3 - 3x^2 - 8x - 10
P(5) = 125 - 75 - 40 - 10 = 0
Thus x-5 is a factor of P(x)

(4) f (x) = x + 2/ x
Domain: x <> 0
Range: -∞ <= f(x) <= -2*sqrt(2), and 2*sqrt(2) <= f(x) <= +∞
The graph is symmetric about the origin.