Algebrahard · Past Paper
If x^2 - 1 is a factor of ax^4 + bx^3 + cx^2 + dx + e, then:
Aa + c + e = b + d = 0
Ba + b + c = d + e
Ca + c + e = 0 and b + d = 0
Da + b + c + d + e = 0
✓ Correct Answer: C — a + c + e = 0 and b + d = 0
Factors are (x-1) and (x+1). P(1)=0 => a+b+c+d+e=0. P(-1)=0 => a-b+c-d+e=0. Subtracting gives 2b+2d=0 => b+d=0. Thus a+c+e=0.
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