12) which of the following is factor of the polynomial x^4+x^3-x^2+x-1
2 answers:
Answer:
none
Step-by-step explanation:
If (x + h) is a factor of f(x) then f(- h) = 0
Given
f(x) = + x³ - x² + x - 1
If (x + 1) is a factor then f(- 1) = 0
f(- 1) = + (- 1)³ - (- 1)² + (- 1) - 1 = 1 - 1 - 1 - 1 - 1 = - 3 ≠ 0
Thus (x + 1) is not a factor
If (x - 1) is a factor then f(1) = 0
f(1) = + 1³ - 1² + 1 - 1 = 1 + 1 - 1 + 1 - 1 = 1 ≠ 0
Thus (x - 1) is not a factor
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