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Factor completely.
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Q. Factor completely.
- Recognize expression type: Recognize the type of expression we are dealing with.The given expression is a quadratic in the form of . We need to determine if it can be factored into a product of two binomials.
- Check for perfect square trinomial: Look for a pattern that might suggest it's a perfect square trinomial.A perfect square trinomial is in the form , which factors into . We need to check if fits this pattern.
- Identify square roots: Identify the square roots of the first and last terms.The square root of the first term, , is . The square root of the last term, , is . Now we check if the middle term, , is twice the product of and .
- Verify middle term: Verify the middle term.Calculate to see if it equals the middle term, .This matches the middle term, so the expression is indeed a perfect square trinomial.
- Write factored form: Write the factored form using the square roots of the first and last terms.Since the expression is a perfect square trinomial, it factors into .
