Question

The zeros of a polynomial function are 1/2, -4 and -1.

What are the factors?

(multiple answers)

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

Answer 1

The factors are
`(x- \frac {\bf 1} {\bf 2}){\bf (x+4)}{\bf (x+1)}`

Explanation:

Given that
`(1)/(2) ,-4, -1` are the zeroes of the polynomial

Let the polynomial be
`P(x)`

For the polynomial
`P(x)`, If r is a zero of
`P(x)` then
`(x-r)` will be a factor of P(x).

If
`(x-r)` is a factor of P(x) then r will be a zero of P(x).

From the given Zeroes we can write it in form of factors as below:

`P(x) = (x- (1)/(2))(x-(-4))(x-(-1))`

`P(x) = (x- (1)/(2))(x+4)(x+1)`