List all of the polynomials of degrees 2 and 3 in Z2[x]. Find all of the irreducible polynomia.s of degrees 2 and 3 in Z2[x].

Which of the following sets of polynomials span R² O A and B OC= {2-3t, 5t+t², −3+ 4t+2t², 1-8t - 2t²} OB and C OB={1-², 1-3t+5t², -3+5t-7t², -4+5t - 6t²} O A = {1,1,²} A and C OA, B and C

Pls help ASAP on all and show all work

7) Find a polynomial function with rational coefficients where some of its zeros are a)-i, 6 b) −1, 4, 1 + i

6. Use the Lagrange interpolating polynomial to find the polynomial passing through the points (1,2), (2,2), (4,1), (5,1).

Let P be a polynomial of odd degree, prove that the range of P is all real numbers.

Find a polynomial of degree 3 that has zeros – 1, – , and 2 such that the coefficents are integers. 2' -

Given the following set S of polynomials, find a polynomial p(x) in P2 so that SU {p(x)} spans P₂ and a non-zero polynomial q(x) in P2 so that SU{q(x)} does not span P2. Use the '^' character to indicate an exponent, e.g. 5x^2–2x+1. 5-|-5x²+4x-9, −8x²-6x+8] p(x) = 0 q(x) = 0