2. 外语
  3. If 1+x + x2 + x3 = 60, then the average(arithmetic mean)of x, x2, x3 , and x4 is equal to which of the following?

If 1+x + x2 + x3 = 60, then the average(arithmetic mean)of x, x2, x3 , and x4 is equal to which of the following?

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问题 If 1+x + x2 + x3 = 60, then the average(arithmetic mean)of x, x2, x3 , and x4 is equal to which of the following?
选项 A、12x
B、15x
C、20x
D、30x
E、60x
答案B
解析 A quick inspection of the answer choices shows that it is not necessary to solve the equation 1 + x + x2 + x3 = 60 for x to answer this question. You are being asked to express the average of the four quantities x, x2, x3, and x4 in terms of x. To express this average in terms of x, you need to add the 4 quantities and divide the result by 4; that is,.
The only information given in the question is that the sum of the 4 quantities, 1 +x+ x2+ x3, is 60, so you need to think of a way to use this information to simplify the expression.
Note that the numerator of the fraction is a sum of 4 quantities, each of which has an x term raised to a power. Thus, the expression in the numerator can be factored as x + x2+ x3+ x4= x(1+ x + x2+ x3). By using the information in the question, you can make the following simplification.

Therefore, the correct answer is Choice B.
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