Chapter 6, Problem 1MCP

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 $x^4\text{ and }(x+1)$ .