16Hit1600
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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