How do you write a polynomial function of least degree with integral coefficients that has the given zeros?

Question

The 1st problem is: 3, 2, -2   & the 2nd problem is: 3, 1, -2,  -4

Answer 1

If a polynomial has zeros at 3, 2 and -2 then this means that 

 

(x-3), (x-2), and (x+2) are all factors of the polynomial  

 

If you multiply these factors together you will get a polynomial with the given zeros 

 

(x-3) * (x-2) * (x+2)

(x-3) * (x^2 - 4)

x^3 -3x^2 - 4x + 12  

 

If you plug in 3, 2 or -2 for x you will see that the polynomial is equal to 0 at those points 

 

The 2nd problem is similar but you will have 4 factors to multiply together