Pregunta
\( x^{2}-3 x-28 \) 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
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( x^{2}-3x-28 = (x-7)(x+4) \)
Solución
Factor the expression by following steps:
- step0: Factor:
\(x^{2}-3x-28\)
- step1: Rewrite the expression:
\(x^{2}+\left(4-7\right)x-28\)
- step2: Rewrite the expression:
\(x^{2}+4x-7x-28\)
- step3: Factor the expression:
\(x\left(x+4\right)-7\left(x+4\right)\)
- step4: Factor the expression:
\(\left(x-7\right)\left(x+4\right)\)
The expression \( x^{2}-3 x-28 \) can be factored as:
\[
(x-7)(x+4)
\]
Therefore, the correct choice is:
A. \( x^{2}-3 x-28=(x-7)(x+4) \)
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Simplifique esta solución 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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