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ValentinkaMS [17]
3 years ago
7

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

Mathematics
2 answers:
GrogVix [38]3 years ago
8 0
None as both leave remainders

brilliants [131]3 years ago
6 0

Answer:

none

Step-by-step 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

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Multiply both the numerator and denominator by 2+\sqrt3, which is called the "conjugate" of 2-\sqrt3:

\dfrac{5+\sqrt3}{2-\sqrt3}\cdot\dfrac{2+\sqrt3}{2+\sqrt3}

Why do we pick this number? Recall the difference of squares factorization:

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Now replace a=2 and b=\sqrt3. Then

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So in your fraction, you end up with

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