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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.______
- Recognize quadratic form: Recognize that the given expression is a quadratic in form, where `x^2` is the variable instead of `x`. The expression can be written as `(x^2)^2 + 2*(3)*(x^2) + 3^2,` which resembles the perfect square trinomial formula `a^2 + 2ab + b^2 = (a +` b)^2.
- Apply perfect square trinomial formula: Apply the perfect square trinomial formula to factor the expression. Since the expression is in the form of `a^2 + 2ab + b^2,` we can write it as `(x^2 +` 3)^2.
- Check factored form: Check the factored form to ensure it matches the original expression by expanding `(x^2 + 3)^2` to verify it equals `x^4 + 6x^2 +` 9.
- Expand and verify: Expanding `(x^2 + 3)^2` gives `(x^2 + 3)(x^2 + 3) = x^4 + 3x^2 + 3x^2 + 9 = x^4 + 6x^2 + 9,` which matches the original expression, confirming the factorization is correct.
- Problem completed: Since the expression `(x^2 + 3)^2` is already factored completely and all coefficients are integers, we have completed the problem.
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