Question

Write a polynomial function with the given zeros x= -2,1,4

Answer 1

With the given zeros x=-2,1,4 the polynomial function is
`x^3-3x^2-6x-8`

Explanation:

Given zeros are x=-2,1,4

Now to find the polynomial function:

With the given zeros we can write it as below:

x=-2 implies that x+2=0

x=-1 implies that x-1=0

x=4 implies that x-4=0

Then we can the zeros or factors by (x+2)(x-1)(x-4)

Now expanding the zeros or factors:

`(x+2)(x-1)(x-4)`

`(x+2)(x-1)(x-4)=(x^2-x+2x-2)(x-4)` ( multiply each term with each term of another factor)

`=(x^2+x-2)(x-4)` ( adding the like terms)

`=x^3-4x^2+x^2-4x-2x+8` ( multiply each term with each term of another factor)

`=x^3-3x^2-6x+8` ( adding the like terms)

`(x+2)(x-1)(x-4)=x^3-3x^2-6x+8`

Therefore the polynomial function is
`(x+2)(x-1)(x-4)=x^3-3x^2-6x+8`

With the given zeros x=-2,1,4 the polynomial function is
`x^3-3x^2-6x-8`