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Factor. _____
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Q. Factor. _____
- Find Common Factors: Look for common factors in each term of the polynomial . Upon inspection, there is no common factor for all terms. However, we can group terms to see if there are common factors within the groups.
- Group Terms: Group the terms to find common factors within the groups.We can group the first two terms and the last two terms: + .Now, let's factor out the common factors within each group.
- Factor First Group: Factor out the greatest common factor from the first group . The greatest common factor is , so we get .
- Factor Second Group: Factor out the greatest common factor from the second group . There is no common factor other than , so this group remains as it is: .
- Write Partially Factored Form: Write down the partially factored form of the polynomial.We have factored the polynomial as far as common factors within groups allow: .
- Look for Patterns: Look for patterns or special products that might help further factor the polynomial. There are no obvious patterns like difference of squares, perfect square trinomials, or sum/difference of cubes that apply to the terms we have. The polynomial does not seem to factor further using standard algebraic techniques.
- Conclude Factoring: Conclude that the polynomial is factored as much as possible with the given techniques. The polynomial is factored to , and no further factoring is possible.
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