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\( x^{2}-3 x-28 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( x^{2}-3 x-28=\square \) B. The expression is prime.

Ask by Riley Bolton. in the United States
Feb 03,2025

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Answer

\( x^{2}-3x-28 = (x-7)(x+4) \)

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Beyond the Answer

To factor the quadratic expression \( x^2 - 3x - 28 \), we need to find two numbers that multiply to -28 (the constant term) and add to -3 (the coefficient of the linear term). The numbers -7 and 4 work perfectly since \(-7 \times 4 = -28\) and \(-7 + 4 = -3\). Therefore, we can express the quadratic as: A. \( x^{2}-3 x-28=(x-7)(x+4) \) Now, let's check if you’ve made a mistake in thinking it might be prime! This expression can indeed be factored, so it’s definitely not prime. Happy factoring!

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