What is polynomial function in standard form with zeros 1, 2, -3, -1

Question

What is polynomial function in standard form with zeros 1, 2, -3, -1

Answer 1

You do this by first writing it in factored form.  Why?  Because they give you the factors!  For the zero 1, the factor is (x-1) because when x = 1 (x-1) = 0.  So:

 

P(x) = (x-1)(x-2)(x+3)(x+1)

 

Multiply it out and simplify by combining like terms to put it into standard form:

 

P(x) = ax⁴ + bx³ + cx² + dx + e