Question
Which expression is equivalent to the polynomial given below? \( 54 x+30 \) A. \( 6(9 x+4) \) B. \( 6(9 x+5) \) C. \( 9(5 x+5) \) D. \( 6(9 x+30) \)
Ask by Moran Stanley. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equivalent expression is \( 6(9x+5) \), choice B.
Solution
1. Factor out the greatest common factor from \(54x + 30\):
\[
54x + 30 = 6(9x) + 6(5)
\]
2. Combine the factors:
\[
54x + 30 = 6(9x + 5)
\]
Thus, the equivalent expression is \( 6(9x+5) \).
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Simplify this solution Beyond the Answer
To find an expression equivalent to \( 54x + 30 \), we can factor out the greatest common factor, which is 6. By factoring, we get: \( 54x + 30 = 6(9x + 5) \) So, the correct answer is B. \( 6(9x + 5) \). This expression simplifies down to the original polynomial when distributed back, making it a neat way to reveal the structure of the polynomial while keeping it fun and engaging through the act of factoring!
