Advanced MathVery hardSum of coefficients from a known factor
Advanced Math practice question
The polynomial p(x) = x³ + ax² − 5x + b, where a and b are constants, has (x − 1) and (x + 2) as factors. What is the value of a + b?
Answer: 4
(x − 1) is a factor, so p(1) = 0: 1 + a − 5 + b = 0 gives a + b = 4. (The other factor fixes a = −2, b = 6.)
Common wrong answers
- If you answered 6
- 6 is b alone.
- If you answered -4
- −4 has the sign wrong.
- If you answered -2
- −2 is a alone.
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