Construct a polynomial function with the following properties: fifth degree, 2 is a zero of multiplicity 4, −4 is the only other zero, leading coefficient is 2.

Answer 1

2(x-2)^4(x+4)

just change the sign of each zero and add x to it. Then multiply them all together, and multiply that by 2

expand if you want

to get a polynomial with leading term 2x^5