Question

Given the following roots x = 2, -3, 4. Write a polynomial function p(x)​

Answer 1

`x^3-3x^2-10x+24`

Explanation:

The first thing that you have to do is take the roots that you're given and write binomial products.

`x= 2, -3, 4`

`(x-2)(x+3)(x-4)`

Remember that a root is the value of "x" in a binomial expression, so the binomial expression itself will have the opposite sign of the root.

The next thing you have to do is multiply the roots together. A good way to do this is the "box method."

(See attachment below for the multiplication of
`(x-2)` and
`x+3`. )

Next, multiply your new trinomial by your remaining binomial. (See additional attachment below for the multiplication of
`(x^2+x-6)` and
`(x-4)`)

The resulting polynomial is
`x^3-3x^2-10x+24`.