2020 · Q49
If (x² − 1) is a factor of ax⁴ + bx³ + cx² + dx + e, then which one of the following is correct?
Elementary MathematicsAlgebra
- Aa + b + c = d + e
- Ba + b + e = c + d
- Cb + c + d = a + e
- Da + c + e = b + d
Explanation
(x² − 1) being a factor means P(1) = 0 and P(−1) = 0: a + b + c + d + e = 0 and a − b + c − d + e = 0. Adding gives a + c + e = 0 and subtracting gives b + d = 0, so a + c + e = b + d. Thus a + c + e = 0 = b + d, so the two sums are equal.