Vega Nunez
12/04/2023 · Senior High School

Select the correct choice below and fill in the answer box within your choice it necessary. A. \( 3 c^{2}-147=3\left(x^{2}-49\right) \) B. The binomial is not factorable.

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To determine whether the expression \( 3c^{2}-147 \) is factorable, we can start by factoring out the common factor. 1. Notice that both terms in \( 3c^{2} - 147 \) have a common factor of 3. We can factor that out: \[ 3c^{2} - 147 = 3(c^{2} - 49) \] 2. Now, we can see that \( c^{2} - 49 \) is a difference of squares, which can be factored further: \[ c^{2} - 49 = (c - 7)(c + 7) \] 3. Therefore, we can write the complete factorization of the original expression: \[ 3c^{2} - 147 = 3(c - 7)(c + 7) \] Since we have successfully factored the expression, the correct choice is: **A. \( 3 c^{2}-147=3\left(x^{2}-49\right) \)** However, it should be noted that the expression should be written as \( 3(c^{2}-49) \) instead of \( 3(x^{2}-49) \). So, the final answer is: **A. \( 3 c^{2}-147=3(c^{2}-49) \)**

Quick Answer

A. \( 3 c^{2}-147=3(c^{2}-49) \)
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