Find the polynomial function the set of zeros below. Assume a stretch factor of a = 1.

Question

-3, 1, 2 - √5i, 2 + √5i

Answer 1

A stretch factor of a=1 means that you multiply the function by 1.  Therefore, your function will be

 

1 * f(x) = (x + 3)(x - 1)(x - [2 - i√5])(x - [2 + i√5])

 

 

Next, we expand the polynomial function.

 

f(x) = (x² + 2x - 3)[x² - x(2 + i√5) - x(2 - i√5) + (4 + 5)]

 

f(x) = (x² + 2x - 3)[x² - 4x + 9]

 

 

Next, think of the first factor as the greatest common factor.  So we rewrite the polynomial as a sum of products.

 

f(x) = x²(x² + 2x - 3) - 4x(x² + 2x - 3) + 9(x² + 2x - 3)

 

 

Finally, distribute and combine like terms to get a polynomial in standard form.  I leave that to you to complete.