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Factor.
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Q. Factor.
- Identify Factors: Identify common factors in all terms.We look for the greatest common factor (GCF) that can be factored out from all terms of the polynomial .The GCF of , , , and is , which means we cannot factor out a common numerical factor. However, there is no common variable factor either, as the constant term does not contain any variable.
- Group for Factoring: Group terms to factor by grouping.Since there is no common factor, we attempt to factor by grouping. We can group the terms as follows: + .Now we look for common factors within each group.
- Factor Grouped Terms: Factor out the common factors from each group.From the first group , we can factor out , which gives us .From the second group , we notice that there is no common factor other than , and the group itself is a binomial that matches the binomial in the first group.So we have .
- Factor Common Binomial: Factor out the common binomial factor.We now have a common binomial factor of in both terms. We can factor this out to get:.
- Check Further Factoring: Check for further factoring possibilities.We need to check if the remaining quadratic can be factored further. This is a sum of squares, which cannot be factored over the real numbers. Therefore, our factoring process is complete.
