Question

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

Factors and multiples

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 $$\displaystyle{P}{\left({x}\right)}=$$.

2021-08-11
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: $$\displaystyle{p}{\left({x}\right)}={x}^{{{3}}}+{5}{x}^{{{2}}}+{25}{x}+{125}$$
$$\displaystyle{p}{\left({x}\right)}={\left({x}^{{{3}}}+{5}{x}^{{{2}}}\right)}+{\left({25}{x}+{125}\right)}$$
$$\displaystyle{p}{\left({x}\right)}={x}^{{{2}}}{\left({x}+{5}\right)}+{25}{\left({x}+{5}\right)}$$
$$\displaystyle{p}{\left({x}\right)}={\left({x}^{{{2}}}+{25}\right)}{\left({x}+{5}\right)}$$