Math help?? Polynomials???

Question

Solve the following polynomial. Enter your solutions as fractions, as needed.
16 x^6 - 24 x^5 = 0
smaller value =
larger value =

Determine the solutions for the following polynomial. Enter your solutions as fractions, as needed.
2 x^4 - 8 x^2 = 0
1stvalue (smallest) =
2nd value =
3rd value (largest) =

I'm really lost as to how to work these out... would appreciate any help?

Answer 1

16 x^6 - 24 x^5 = 0

Factor:

8x^5(2x - 3) = 0

Therefore,

8x^5 = 0 or
2x - 3 = 0

(if the product of two or more expressions is zero, one or another of the expressions must be zero; so set each expression of the product to zero)

The solutions of those two equations will give you the smaller and larger values.

2 x^4 - 8 x^2 = 0

Same process. First, factor:

2x^2(x^2 - 4) = 0
2x^2(x-2)(x+2) = 0

Therefore,
2x^2 = 0 or
x - 2 = 0 or
x + 2 = 0