Problem 15 - 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. $$4 y-4$$

Step-by-Step Solution

Answer

The factorized form of the polynomial \(4y - 4\) is \(4(y-1)\).

Step 1: Identify the GCF

The polynomial is \(4y - 4\). The terms are \(4y\) and \(-4\). The greatest common factor of these two terms is \(4\).

Step 2: Divide each term by the GCF

Now, we take the GCF and divide each term in the polynomial by this factor. So, \(4y/4 = y\) and \(-4/4 = -1\).

Step 3: Write out the factorized form

Finally we want to write the polynomial in its factorized form. This is done by multiplying the GCF with the new terms obtained in step 2. Hence, the factorized form of the polynomial is \(4(y-1)\).