Rationale and polynomial

1. For the polynomial y = 4x3 – 3x – 1

a. List all possible rational roots

b. Find all rational zeros of the polynomial algebraically

c. State the multiplicity of each zero

d. Write the polynomial in complete factored form

2. For the polynomial y = -2x(x – 1)2(x – 3)2

a. State the end behavior.

b. State the domain and range.

c. Determine the possible number of turning points.

d. List all zeros, their multiplicities and whether each x-intercept touches the graph crosses through the x-axis or just touches the x-axis.

e. Graph the polynomial using the details found above

3. Find the polynomial function with the given zeros of -2, 0 and 2, whose graph passes through the point (-4, 16). Do not keep in factored form; write polynomial in standard form.
4. Solve the inequality 3x2 + 2x – 8 < 0.