Question

Which polynomial function has zeros at 2, −4, and 1?

y = (x + 2)(x − 4)(x + 1)
y = (x − 2)(x − 4)(x + 1)
y = (x + 2)(x + 4)(x − 1)
y = (x − 2)(x + 4)(x − 1)

Answer 1

y = (x - 2)(x + 4)(x - 1)

Explanation:

Given the zeros of a function say x = a and x = b, then

The factors are (x - a) and (x - b) and

y = (x - a)(x - b)

Given the zeros are x = 2, x = - 4, x = 1, then

the factors are (x - 2), (x - (- 4)) and (x - 1), that is

(x - 2), (x + 4), (x - 1) , thus

y = (x - 2)(x + 4)(x - 1)

Answer 2

`y(x) = (x-2) (x-(-4)) (x-1)`

And if we implify we got:

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

And the correct option would be:

y = (x − 2)(x + 4)(x − 1)

Explanation:

For this case we want a polynomial that satisfy the following zeros:

`X= 2,-4,1`

So then we need a polynomial of grade 3, and we can find the polynomial with this general formula:

`y(x) = (x -a) (x-b) (x-c) ..... (x-k)`

Where
`a,b,c,...,k` represent the possible roots for the polynomial, if we replace we got:

`y(x) = (x-2) (x-(-4)) (x-1)`

And if we implify we got:

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

And the correct option would be:

y = (x − 2)(x + 4)(x − 1)