Factor x^4 + 8x^2 + 16 completely. All factors in your answer should have integer coefficients. ______

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Factor x^4 + 8x^2 + 16 completely.  All factors in your answer should have integer coefficients. ______

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Identify Polynomial: We are given the polynomial x^4 + 8x^2 + 16 and asked to factor it completely. The polynomial resembles a perfect square trinomial, which has the form (a^2 + 2ab + b^2) = (a + b)^2. 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 x^4, which is the square of x^2. So, we have a = x^2.Identify Square of Last Term: Next, we identify the square of the last term. The last term of the polynomial is 16, which is the square of 4. So, we have b = 4.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 8x^2, and for a perfect square trinomial, the middle term should be 2ab. We have a = x^2 and b = 4, so 2ab = 2 * x^2 * 4 = 8x^2, 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 (a + b), where a = x^2 and b = 4. Therefore, the polynomial can be factored as (x^2 + 4)^2.Check Further Factorization: Finally, we check if the binomial (x^2 + 4) can be factored further with integer coefficients. Since x^2 + 4 does not have real roots and cannot be factored over the integers, we conclude that (x^2 + 4)^2 is the complete factorization of the polynomial.

Factor $x^4 + 8x^2 + 16$ completely. $\newline$ All factors in your answer should have integer coefficients. $\newline$ ______

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Factor x4+8x2+16x^4 + 8x^2 + 16x4+8x2+16 completely.\newlineAll factors in your answer should have integer coefficients.\newline______

Factor $x^4 + 8x^2 + 16$ completely. $\newline$ All factors in your answer should have integer coefficients. $\newline$ ______