Can anybody help me withANY of these Algebra Questions?

Question

1.) Use the Rational Zero Theorem to list all possible rational zeros of b(x) = 2x^6 + 3x^5 + 5x^3 + 9x^2 -3

THE NEXT PROBLEMS: Find all zeros, roots, intercepts or solutions of the given polynomials.

2.) I(x)= x^3 +6x^2 - x - 6

3.) N(x)= 2x^3 + 5x^2 - x - 4

4.) p(x)= 6x^4 - 11x^3 + 2x^2 + 5x - 2

Please show me your work so I know How to do these in the future.

!!!THANK YOU EVERYONE!!!

Answer 1

1.) Rational root theorem: For every polynomial, every rational solution will equal +/- p/q, where p is a factor of the constant term (with no variable) of the polynomial, and q is a factor of the highest degreed term.

For: b(x) = 2x^6 + 3x^5 + 5x^3 + 9x^2 -3
p = -3 (factors: (3, 1)
q = 2 (factors: (2.1)

All factors will equal +/- p/q: 3/1, 3/2, 1/2, 1, -3/1, -3/2, -1/2, -1