Chapter 8.5, Problem 10WE

To determine

To find: if the binomial is a factor of the provided polynomial

Answer to Problem 10WE

The binomial $t+1$ is a factor of the provided polynomial $P\left(t\right)=t^5+t^4+t^3+t^2+t+1$

Explanation of Solution

Given information: the polynomial and binomial provided in the question,

  $t+1;P\left(t\right)=t^5+t^4+t^3+t^2+t+1$

Calculation:

Use the factor theorem, $P\left(-1\right)=0$ ,

  $\begin{array}{l}P\left(-1\right)={\left(-1\right)}^5+{\left(-1\right)}^4+{\left(-1\right)}^3+{\left(-1\right)}^2+\left(-1\right)+1\\ =-1+1-1+1-1+1\\ =0\end{array}$

Hence, the binomial $t+1$ is a factor of the provided polynomial $P\left(t\right)=t^5+t^4+t^3+t^2+t+1$