Advanced MathHardRemainder from a polynomial identity
Advanced Math practice question
A polynomial p satisfies p(x) = (x − 2)q(x) + 5 for all x, where q is another polynomial. What is the value of p(2)?
Answer: 5
At x = 2 the factor (x − 2) is 0, so p(2) = 0 · q(2) + 5 = 5.
Common wrong answers
- If you answered 0
- 0 forgets the +5.
- If you answered 2
- 2 is the input, not the output.
- If you answered 7
- 7 adds 2 to 5 as if q(2) were 1 and the factor were 2.
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