Write a polynomial function f of least degree that has a leading coefficient of 1 and the given zeros. Write the function in standard form. −4,−2,5

Question

Write a polynomial function f
of least degree that has a leading coefficient of 1 and the given zeros. Write the function in standard form.

−4,−2,5

F(x)=

Answer 1

f(x) = (x+4)(x+2)(x-5)

Note that if x = -4, -2, or 5 then f(x)=0

 

f(x) = (x²+6x+8)(x-5) =

 

x³ - 5x²

    +6x² - 30x

            + 8x  - 40

--------------------

x³ + x² - 22x - 40

 

f(x) = x³ + x² - 22x - 40

Answer 2

F(x) = (x + 4)(x + 2)(x - 5)

 

 

Just expand to get it in standard form.