Question

12) which of the following is factor of the polynomial x^4+x^3-x^2+x-1

x+1
x-1
Both options 1 and 2
None​


please answer friends

Answer 1

None as both leave remainders

Answer 2

none

Explanation:

If (x + h) is a factor of f(x) then f(- h) = 0

Given

f(x) =
`x^(4)` + x³ - x² + x - 1

If (x + 1) is a factor then f(- 1) = 0

f(- 1) =
`(-1)^(4)` + (- 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) =
`1^(4)` + 1³ - 1² + 1 - 1 = 1 + 1 - 1 + 1 - 1 = 1 ≠ 0

Thus (x - 1) is not a factor