Question

Find a polynomial function P(x)with the given zeros.4, 3, 8

Answer 1

Given the word problem, we can deduce the following information:

The zeroes are: 4, 3, 8

To determine the polynomial function P(x) with the given zeroes, we follow the process as shown below:

`\begin{gathered} (x-4)(x-3)(x-8)=0 \\ \\ \end{gathered}`

We first expand (x-4)(x-3):

`(x-4)(x-3)=x^2-7x+12`

Next, we expand (x^2-7x+12)(x-8):

`\begin{gathered} (x^2-7x+12)(x-8)=x^2(x)+x^2(-8)-7x(x)-7x(-8)+12(x)+12(-8) \\ Simplify \\ =x^3-15x^2+68x-96 \end{gathered}`

Hence,

`x^3-15x^2+68x-96=0`

Therefore, the polynomial function is:

`P(x)=x^3-15x^2+68x-96`