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Popular >

factor x^4-2x^3+2x-1

Solution

factor

x^{4} - 2 x^{3} + 2 x - 1

Solution

(x - 1)^{3} (x + 1)

Solution steps

x^{4} - 2 x^{3} + 2 x - 1

Use the rational root theorem

= (x - 1) \frac{x ^{4} - 2 x ^{3} + 2 x - 1}{x - 1}

\frac{x ^{4} - 2 x ^{3} + 2 x - 1}{x - 1} = x^{3} - x^{2} - x + 1

= (x - 1) (x^{3} - x^{2} - x + 1)

Factor

x^{3} - x^{2} - x + 1 : (x - 1) (x + 1) (x - 1)

= (x - 1) (x - 1) (x + 1) (x - 1)

Apply exponent rule:

aaa = a^{3}

(x - 1) (x - 1) (x - 1) = (x - 1)^{3}

= (x - 1)^{3} (x + 1)

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Frequently Asked Questions (FAQ)

What is factor x^4-2x^3+2x-1 ?
The solution to factor x^4-2x^3+2x-1 is (x-1)^3(x+1)