16Hit1600
Advanced MathVery hardFactoring a difference of shifted powers

Advanced Math practice question

The expression 2^(x + 2) − 2ˣ is equivalent to k·2ˣ, where k is a constant. What is the value of k?

Answer: 3

2^(x + 2) = 4·2ˣ, so the difference is 4·2ˣ − 2ˣ = 3·2ˣ.

Common wrong answers

If you answered 1
1 subtracts exponents instead of expressions.
If you answered 2
2 treats 2^(x + 2) as 2·2ˣ.
If you answered 4
4 forgets to subtract the 2ˣ.

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