What is factor x^5-3x^4+12x^3-28x^2+27x-9 ?

The solution to factor x^5-3x^4+12x^3-28x^2+27x-9 is (x-1)^3(x^2+9)

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factor x^5-3x^4+12x^3-28x^2+27x-9

factor

x^{5} - 3 x^{4} + 12 x^{3} - 28 x^{2} + 27 x - 9

(x - 1)^{3} (x^{2} + 9)

Solution steps

x^{5} - 3 x^{4} + 12 x^{3} - 28 x^{2} + 27 x - 9

Use the rational root theorem

= (x - 1) \frac{x ^{5} - 3 x ^{4} + 12 x ^{3} - 28 x ^{2} + 27 x - 9}{x - 1}

\frac{x ^{5} - 3 x ^{4} + 12 x ^{3} - 28 x ^{2} + 27 x - 9}{x - 1} = x^{4} - 2 x^{3} + 10 x^{2} - 18 x + 9

= (x - 1) (x^{4} - 2 x^{3} + 10 x^{2} - 18 x + 9)

Factor

x^{4} - 2 x^{3} + 10 x^{2} - 18 x + 9 : (x - 1) (x - 1) (x^{2} + 9)

= (x - 1) (x - 1) (x - 1) (x^{2} + 9)

Apply exponent rule:

aaa = a^{3}

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

= (x - 1)^{3} (x^{2} + 9)

6 (x - 1) = 3 x + 7 + 3 x

- 3 - ∣ 5 - 2 x ∣ < - 11

7 + 4 (1 + 8 z) = 17

3 x^{2} + x - 2 = 0

x^{2} - ∣ x - 1 ∣ - 1 = 0

What is factor x^5-3x^4+12x^3-28x^2+27x-9 ?
The solution to factor x^5-3x^4+12x^3-28x^2+27x-9 is (x-1)^3(x^2+9)