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Factor completely.All factors in your answer should have integer coefficients.______
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Q. Factor completely.All factors in your answer should have integer coefficients.______
- Identify Polynomial: We are given the polynomial and asked to factor it completely. The polynomial resembles a perfect square trinomial, which has the form . We will attempt to express the given polynomial in this form.
- Identify Square of First Term: First, we identify the square of the first term. The first term of the polynomial is , which is the square of . So, we have .
- Identify Square of Last Term: Next, we identify the square of the last term. The last term of the polynomial is , which is the square of . So, we have .
- Check Middle Term: Now, we check if the middle term of the polynomial fits the pattern of a perfect square trinomial. The middle term is , and for a perfect square trinomial, the middle term should be . We have and , so , which matches the middle term of the polynomial.
- Write as Square of Binomial: Since the polynomial fits the pattern of a perfect square trinomial, we can write it as the square of a binomial. The binomial is , where and . Therefore, the polynomial can be factored as .
- Check Further Factorization: Finally, we check if the binomial can be factored further with integer coefficients. Since does not have real roots and cannot be factored over the integers, we conclude that is the complete factorization of the polynomial.
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