Problem 33 - 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. $$12 y^{2}+16 y-8$$

Step-by-Step Solution

Answer

The polynomial \(12y^{2} + 16y - 8\) factored using the greatest common factor is \(4(3y^{2} + 4y - 2)\).

Step 1: Identify the Greatest Common Factor

Looking at the polynomial, \(12y^{2} + 16y - 8\), the coefficients are 12, 16 and -8. The greatest number that divides into these three numbers evenly is 4. So, the greatest common factor is 4.

Step 2: Factor out the Greatest Common Factor

Divide each term in the original polynomial by the identified greatest common factor, 4. This gives the following: \(4(3y^{2} + 4y - 2)\).

Step 3: Check the Result

Finally, check to ensure that the factored form cannot be factored further. After checking, it is observed that \(3y^{2} + 4y - 2\) has no common factors other than 1 so, it cannot be factored further. The factored form of the polynomial is thus \(4(3y^{2} + 4y - 2)\).