Chapter 6, Problem 1MCP

In Exercises 1-13, factor completely, or state that the polynomial is prime.

1. $x^5+x^4$

To determine

The factor completely or state that the polynomial is prime

Answer to Problem 1MCP

Solution:

   $x^4(x+1)$

Explanation of Solution

Given:

The polynomial is $x^5+x^4$.

Calculation:

Consider the polynomial $x^5+x^4$.

We have to completely factor the polynomial.

The terms of the polynomial are $x^5,x^4$.

Greatest common factor for the polynomial is $x^4$.

Factor out the greatest common factor for the polynomial, then we get that,

   $x^5+x^4=x^4(x+1)$

Conclusion:

Therefore, factors of $x^5+x^4$ are $x^4\text{ and }(x+1)$.