Question

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

Answer 1

Answer:

1)

$x^{3} - 3timesx -2 = 0$

2)

$x^{3} - x^{2} - 6timesx$

Step-by-step 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,

$g(x) = (x + 2)(x - 0)(x - 3) = (x^{2} + 2timesx )(x - 3) = x^{3} + 2timesx^{2} - 3timesx^{2} -6timesx = x^{3} - x^{2} - 6timesx$