Question

Write a polynomial function with the given zeros. multiply the terms (write in standard form).

1) x= -1, -1, 2

2) x= -2, 0, 3

Answer 1

1)

`x^(3) - 3timesx -2 = 0`

2)

`x^(3) - x^(2) - 6timesx`

Explanation:

1)

A polynomial function of x can be represented as

`f(x) = (x + 1)(x + 1)(x - 2)`, if we put x = -1 / -1 / 2, then we will get x = 0.

Now,

`f(x) = (x + 1)(x + 1)(x - 2) = (x^(2) + 2timesx + 1)(x - 2) = x^(3) + 2timesx^(2) + x - 2timesx^(2) - 4timesx -2 = x^(3) - 3timesx -2.`

2)

Similarly, this function must have to be valued 0 for x = -2, 0, 3

Let g(x) be the function.

Hence,

`g(x) = (x + 2)(x - 0)(x - 3) = (x^(2) + 2timesx )(x - 3) = x^(3) + 2timesx^(2)  - 3timesx^(2) -6timesx =  <strong>x^(3) - x^(2) - 6timesx</strong>`