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{:("Column A"," ", "Column B"),("The...

`{:("Column A"," ", "Column B"),("The largest power of 3 that is a factor of "5.3^2 + 3^2. 2,," The largest power of 3 that is a factor of "3.2+7.3""):}`

A

If column A is larger

B

If column B is larger

C

If the columns are equal

D

If there is not enough information to decide

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to determine the largest power of 3 that is a factor of the expressions given in Column A and Column B. ### Step-by-Step Solution: **Column A:** 1. **Expression:** \( 5 \cdot 3^2 + 3^2 \cdot 2 \) 2. **Factor out \( 3^2 \):** \[ 3^2(5 + 2) = 3^2 \cdot 7 \] 3. **Identify the power of 3:** The largest power of 3 that is a factor of this expression is \( 3^2 \), which means the power is 2. **Column B:** 1. **Expression:** \( 3 \cdot 2 + 7 \cdot 3 \) 2. **Factor out 3:** \[ 3(2 + 7) = 3 \cdot 9 \] 3. **Rewrite 9 as a power of 3:** \[ 3 \cdot 9 = 3 \cdot 3^2 = 3^3 \] 4. **Identify the power of 3:** The largest power of 3 that is a factor of this expression is \( 3^3 \), which means the power is 3. ### Comparison: - Column A has a largest power of 3 as 2. - Column B has a largest power of 3 as 3. Since \( 3 > 2 \), we conclude that Column B is larger. ### Final Answer: Column B is larger.
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If x-a is a factor of x^3-3x^2a+2a^2x+b , then the value of b is (a) 0 (b) 2 (c) 1 (d) 3