The zeros of the equation is given below as
[tex]-2,4,5[/tex]
Step 1:
Express the zeros as factors of the polynomial P(x), we will have
[tex]\begin{gathered} x=-2 \\ (x+2) \end{gathered}[/tex][tex]\begin{gathered} x=4 \\ (x-4) \end{gathered}[/tex][tex]\begin{gathered} x=5 \\ (x-5) \end{gathered}[/tex]
Step 2:
Multiply the first two factors by expanding them
[tex]\begin{gathered} (x+2)(x-4) \\ x(x-4)+2(x-4) \\ x^2-4x+2x-8 \\ (x^2-2x-8) \end{gathered}[/tex]
Step 3 :
Multiply the expression gotten in step 2 by (x-5) from step 1
[tex]\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}[/tex]
Therefore,
The final answer is
[tex]P(x)=x^3-7x^2+2x+40[/tex]
