Advanced MathHardFactoring a difference of consecutive powers
Advanced Math practice question
The function f is defined by f(x) = 3ˣ − 3^(x − 1). For every value of x, f(x) can be written as k · 3^(x − 1), where k is a constant. What is the value of k?
Answer: 2
3ˣ = 3 · 3^(x − 1), so f(x) = 3 · 3^(x − 1) − 3^(x − 1) = 2 · 3^(x − 1). Thus k = 2.
Common wrong answers
- If you answered 0
- 0 assumes the two terms are equal.
- If you answered 1
- 1 comes from 3ˣ − 3^(x − 1) = 3^(x − (x − 1)) = 3¹, wrongly subtracting exponents.
- If you answered 3
- 3 is the factor relating 3ˣ to 3^(x − 1), before subtracting the second term.
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