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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Step-by-step Solution
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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