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Factor as the product of two binomials.
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Q. Factor as the product of two binomials.
- Check for Perfect Square Trinomial: Determine if the quadratic can be factored as a perfect square trinomial.A perfect square trinomial is in the form , where is the square root of the first term and is the square root of the last term. We need to check if the middle term is twice the product of the square roots of the first and last terms.The first term is , which is a perfect square of .The last term is , which is a perfect square of .The middle term is , which is twice the product of and ().Since the middle term is indeed twice the product of the square roots of the first and last terms, the quadratic is a perfect square trinomial.
- Write as Square of Binomial: Write the quadratic as the square of a binomial.Since we have a perfect square trinomial, we can write it as the square of a binomial.The square root of the first term, , is .The square root of the last term, , is .The middle term is negative, so we use a minus sign in the binomial.The factored form is .
