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Factor completely.Answer:
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Q. Factor completely.Answer:
- Identify coefficients: Identify the coefficients , , and in the quadratic expression . By comparing with the standard form , we find that , , and .
- Find two numbers: Find two numbers that multiply to () and add up to ().We need to find two numbers that multiply to and add up to . The numbers and fit this requirement because and .
- Rewrite middle term: Rewrite the middle term using the two numbers found in Step .We can express as the sum of and . Therefore, we rewrite the expression as .
- Factor by grouping: Factor by grouping.We group the terms as follows: + .Now we factor out the common factors from each group.From the first group, we can factor out , giving us .From the second group, we can factor out , giving us .
- Write factored form: Write the factored form of the expression.Since both groups contain the factor , we can factor this out to get the final factored form of the expression: .
