Problem 14 - 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. $$9 x+9$$

Step-by-Step Solution

Answer

The factored form of the polynomial \(9x + 9\) is \(9(x + 1)\)

Step 1: Identify the Greatest Common Factor (GCF)

Examine the coefficients of all the terms in the polynomial and find the highest number that divides them all evenly. In the given polynomial \(9x + 9\), 9 is a common factor to both terms.

Step 2: Factor out the GCF

By factoring out, we mean dividing each term in the polynomial by the GCF and writing the polynomial as the product of the GCF and the resulting expression. For the polynomial \(9x + 9\), when factoring out the GCF 9, it becomes \(9(x + 1)\).

Step 3: Verify Your Solution

To make sure that the solution is correctly factored, distribute the GCF back through the parenthesis. It should return the original expression. For our solution, distributing back, \(9(x + 1)\) reverts to the initial polynomial \(9x + 9\). Hence, the factoring is correct