What is factor x^4-3x^3-9x^2+23x-12 ?

The solution to factor x^4-3x^3-9x^2+23x-12 is (x-1)^2(x+3)(x-4)

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factor x^4-3x^3-9x^2+23x-12

factor

x^{4} - 3 x^{3} - 9 x^{2} + 23 x - 12

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

Solution steps

x^{4} - 3 x^{3} - 9 x^{2} + 23 x - 12

Use the rational root theorem

= (x - 1) \frac{x ^{4} - 3 x ^{3} - 9 x ^{2} + 23 x - 12}{x - 1}

\frac{x ^{4} - 3 x ^{3} - 9 x ^{2} + 23 x - 12}{x - 1} = x^{3} - 2 x^{2} - 11 x + 12

= (x - 1) (x^{3} - 2 x^{2} - 11 x + 12)

Factor

x^{3} - 2 x^{2} - 11 x + 12 : (x - 1) (x + 3) (x - 4)

= (x - 1) (x - 1) (x + 3) (x - 4)

Apply exponent rule:

aa = a^{2}

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

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

3^{- 12}

11 + (- 4)

- 4 (x + 3)

(2 s + 3)^{3}

What is factor x^4-3x^3-9x^2+23x-12 ?
The solution to factor x^4-3x^3-9x^2+23x-12 is (x-1)^2(x+3)(x-4)