3,2,-2 writing polynomials from zeros answer it with work please

Question

i have this problem and i have to write a polynomial with given zeroes please answer this question and show work thanks.

Answer 1

Use the factored form:

 

y = a(x-3)(x+2(x-2)

 

where a = any real number.  If you are to choose a polynomial, choose a = 1.  Each binomial factor equates to one zero:

• When x = 3, the factor (x-3) = (3-3) = 0
• When x = 2, then (x-2) = (2-2) = 0
• When x = -2, then (x+2) = (-2+2) = 0.

 

Multiply the factored from out to put the polynomial into standard form.

Answer 2

Assuming it is a polynomial of degree 3, just multiply factors of the form x - x_i, where the x_i are the zeros.

 

f(x) = (x - 3)(x - 2)([x - (-2)] = (x - 3)(x - 2)(x + 2)

 

You can also multiply by any real number ≠ 0.

 

g(x) = a(x - 3)(x - 2)(x + 2),

a ≠ 0

 

You can expand the functions to standard form if you wish.