Question

Need help with this. The polynomial needs to be written in standard form.

Answer 1

`\begin{gathered} A\text{ polynomial has a }\alpha\text{ as a zero if and only if (x-}\alpha)\text{ is a factor of the polynomial:} \\ P(x)=(x-18)(x+10i)(x-10i) \\ P(x)=(x-18)(x^2-10xi+10xi-100i^2) \\ i^2=-1^{} \\ P(x)=(x-18)(x^2+100) \\ P(x)=x^3+100x-18x^2-1800 \\ P(x)=x^3-18x^2+100x-1800 \\ \text{And as a final step when x=1 it has a value of -3434} \\ P(x)=x^3-18x^2+100x-1800-1717 \\ P(x)=x^3-18x^2+100x-3517 \end{gathered}`