Problem 17 - 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. $$5 x+30$$

Step-by-Step Solution

Answer

The factorized form of the polynomial \(5x + 30\) is \(5(x + 6)\).

Step 1: Identify the Greatest Common Factor (GCF)

In the polynomial \(5x + 30\), we have two terms: \(5x\) and \(30\). Let's evaluate each term individually and see if there's a common factor. A quick observation reveals that both terms are divisible by '5'. Thus, '5' is the greatest common factor (GCF).

Step 2: Divide each term by the GCF

Now that the GCF has been identified, the next step in factorization is to divide each term of the polynomial by the GCF. So, \(5x\) divided by '5' results in 'x' and \(30\) divided by '5' yields '6'.

Step 3: Write the factorized form of the polynomial

The final step is to put the factorized terms together to get the factorized form of the polynomial. We multiply the GCF '5' with the result obtained in step 2. So, the factorized form of the polynomial \(5x + 30\) will be \(5(x + 6)\).