write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the function in standard form. -2,3,6

A polynomial function f of least degree  = f = x³ - 7x² + 36

The function in standard form = f = x³ - 7x² + 36

Step-by-step explanation:

As given, Leading coefficient of polynomial function = 1

Also given, zeroes of the function = -2, 3, 6

for root -2 : (x - (-2)) = (x + 2)

for root 3 : ( x - 3)

for root 6 : (x - 6)

Therefore, the polynomial function becomes -

f = 1(x+2)(x-3)(x-6)

⇒f = (x+2)(x² - 6x - 3x + 18)

⇒f = (x+2)(x² - 9x + 18)

⇒f = x³ - 9x² + 18x + 2x² - 18x + 36

⇒f = x³ - 7x² + 36