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Factor.
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Q. Factor.
- Identify , , : Identify , , and in the quadratic expression . Compare with .
- Find Factors and Sum: Find two numbers that multiply to (which is ) and add up to (which is ).We need to find two numbers that satisfy these conditions.After checking possible pairs of factors of , we find that there are no such integers that multiply to and add up to .
- Factor by Grouping: Since we cannot find integers that satisfy the conditions, we attempt to factor by grouping or check if the quadratic is a perfect square trinomial.We can rewrite the expression as and try to factor by grouping.
- Factor Common Factors: Factor out the greatest common factor from each group.From , we can factor out , which gives us .From , we can factor out , which gives us .Now we have .
- Factor Common Binomial: Factor out the common binomial factor . We can write the expression as .
- Verify Factored Form: Verify the factored form by expanding it to ensure it equals the original expression. .The expanded form matches the original expression, so the factoring is correct.
