Question

I need help with this question please. Just apart of a practice

Answer 1

The zeros of the equation is given below as

`-2,4,5`

Step 1:

Express the zeros as factors of the polynomial P(x), we will have

`\begin{gathered} x=-2 \\ (x+2) \end{gathered}`
`\begin{gathered} x=4 \\ (x-4) \end{gathered}`
`\begin{gathered} x=5 \\ (x-5) \end{gathered}`

Step 2:

Multiply the first two factors by expanding them

`\begin{gathered} (x+2)(x-4) \\ x(x-4)+2(x-4) \\ x^2-4x+2x-8 \\ (x^2-2x-8) \end{gathered}`

Step 3 :

Multiply the expression gotten in step 2 by (x-5) from step 1

`\begin{gathered} (x^2-2x-8)(x-5) \\ P(x)=x(x^2-2x-8)-5(x^2-2x-8) \\ P(x)=x^3-2x^2-8x-5x^2+10x+40 \\ P(x)=x^3-2x^2-5x^2-8x+10x+40 \\ P(x)=x^3-7x^2+2x+40 \end{gathered}`

Therefore,

The final answer is

`P(x)=x^3-7x^2+2x+40`