Question

Given \(\displaystyle{P}{\left({x}\right)}={x}^{{{3}}}+{5}{x}^{{{2}}}+{25}{x}+{125}\), find the zeros, real and non-real of P.
The zeros are 5.
Write P in factored form (as a product of linear factors). Be sure to write the full equation, including \(\displaystyle{P}{\left({x}\right)}=\).

Answer 1

Step 1
Given \(\displaystyle{P}{\left({x}\right)}={x}^{{{3}}}+{5}{x}^{{{2}}}+{25}{x}+{125}\)
We have to write P in factored from
Step 2
given: \(\displaystyle{p}{\left({x}\right)}={x}^{{{3}}}+{5}{x}^{{{2}}}+{25}{x}+{125}\)
\(\displaystyle{p}{\left({x}\right)}={\left({x}^{{{3}}}+{5}{x}^{{{2}}}\right)}+{\left({25}{x}+{125}\right)}\)
\(\displaystyle{p}{\left({x}\right)}={x}^{{{2}}}{\left({x}+{5}\right)}+{25}{\left({x}+{5}\right)}\)
\(\displaystyle{p}{\left({x}\right)}={\left({x}^{{{2}}}+{25}\right)}{\left({x}+{5}\right)}\)