Question

Create the polynomial which has roots 3and 2

Answer 1

f(x) = x² - 5x + 6

Explanation:

Given a root of a polynomial x = a then the factor is (x - a)

Here the roots are x = 3 and x = 2 , thus the corresponding factors are

(x - 3) and (x - 2)

The polynomial is then the product of the factors, that is

f(x) = (x - 3)(x - 2) ← expand using FOIL

= x² - 5x + 6

Answer 2

Since this polynomial has answers 3 and 2, we can set up the equation (x-3)(x-2) = 0

That’s already our answer, but if you want it in standard form, We can use FOIL to multiply the 2 expressions:
(x-3)(x-2)
=x^2-3x-2x+6
=x^2-5x+6