Question 382648
The first problem is a difference of two cubes.
The formula for this is {{{x^3 - y^3=(x-y)(x^2+xy+y^2)}}}
For your problem, 2a+b will be used in place of x, and b will be used in place of y.
{{{((2a+b)-b)((2a+b)^2+(2a+b)b+b^2)}}}
Simplify: {{{(2a)(4a^2+4ab+b^2+2ab+b^2+b^2)}}}
Combine like terms: {{{(2a)(4a^2+6ab+3b^2)}}}
That is the final answer :)
For a polynomial to have specific zeros, you'll have to say x = whatever the zero is.  Here, x=0, x=1, and {{{x=3-sqrt(5)}}}.  For each of these, get everything to the same side so that each one equals 0.  x=0, x-1=0, and {{{x-3+sqrt(5)=0}}}.  The polynomial function is the product of these: {{{f(x)=x*(x-1)*(x-3+sqrt(5))}}}.  You can multiply this out to make it look more like a typical polynomial.