Problem 21 - Introductory Algebra for College Students

Question

Factor each polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. $$x^{2}+5 x$$

Step-by-Step Solution

Answer

The factorized form of the polynomial \(x^{2}+5 x\) using the greatest common factor is \(x * (x+5)\).

Step 1: Identify the Common Factor

In the polynomial, \(x^{2}+5 x\), the common factor in both of the terms is 'x' as both terms contain this variable.

Step 2: Factorize the Polynomial

Once the common factor is identified, put this common factor out in front and open parenthesis. Place the terms that are left when you divide each term of the polynomial by the greatest common factor, inside the parenthesis. Doing that for \(x^{2}+5 x\), we get: \(x * (x+5)\). Here, 'x' is the greatest common factor and 'x+5' is the quotient when you divide the original polynomial by the common factor 'x'.