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factor as the product of two binomials.
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Q. factor as the product of two binomials.
- Identify Coefficients: Identify the coefficients of the quadratic expression.The quadratic expression is . Here, the coefficient of is , the coefficient of is , and the constant term is .
- Find Multiplying Numbers: Determine two numbers that multiply to give the product of (which is ) and add up to (which is ).We need to find two numbers that multiply to and add up to . The numbers and satisfy these conditions because and .
- Write Split Expression: Write the quadratic expression using the two numbers found in the previous step to split the middle term.The expression becomes . We have split the middle term into and .
- Factor by Grouping: Factor by grouping.Group the terms to factor by grouping: .
- Factor Common Factors: Factor out the greatest common factor from each group.From the first group , we can factor out an to get . From the second group , we can factor out a to get .
- Write Factored Form: Write the factored form by combining the common factors.Since both groups contain the factor , the factored form is .
