A) Factor f(x)=x^3-x^2-10x-8. Determine sum of zeros and product of zeros. Now determine sum of all double products of zeros (i.e., determine r1r2+r1r3+r2r3). Find relationship between these 3 values and coefficients of polynomial?
B) Assume monic (leading coefficient 1) cubic polynomial function f(x)=x^3+bx^2+cx+d has zeros r1, r2, r3. Write polynomial factored form and multiply factors. Write relationships between coefficients of every form of polynomial.
C) Assume monic Quaric polynomial function f(x)=x^4+bx^3+cx^2+dx+e has zeros r1, r2, r3, r4. Repeat part B for polynomial function.
D) What relationship find between zeros of polynomial function and coefficients of monic polynomial function? Will the formulas always work? Describe. Why do you believe having formulas like this would be useful? Describe.