SOLUTION: Write the simplest polynomial function with the given zeros (-2, 2, 4)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Write the simplest polynomial function with the given zeros (-2, 2, 4)      Log On


   

Question 247328: Write the simplest polynomial function with the given zeros (-2, 2, 4)
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


If a number is a zero of a polynomial, then the binomial is a factor of the polynomial. The simplest polynomial function with the given zeros is the polynomial function with the three factors that correspond to the three given zeros. Since there are three zeros, the polynomial function must be of the third degree.

John

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Write the simplest polynomial function with the given zeros (-2, 2, 4)

The simplest polynomial function with real zeros 

z1, z2, z3, ... zn 

is found by starting with 

P(x) = (x-z1)(x-z2)...(x-zn)

and multiplying it out.

So the simplest polynomial function with xeros -2, 2, and 4 is

P(x) = [x-(-2)](x-2)(x-4)

P(x) = [x+2](x-2)(x-4)

P(x) = (x+2)(x-2)(x-4)

P(x) = (x2-2x+2x-4)(x-4)

P(x) = (x2-4)(x-4)

P(x) = x3-4x2-4x+16

Edwin