What is (x^4-3x^3+6x^2-12x+8)/(x-1) ?

The solution to (x^4-3x^3+6x^2-12x+8)/(x-1) is (x-2)(x^2+4)

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simplify (x^4-3x^3+6x^2-12x+8)/(x-1)

simplify

\frac{x ^{4} - 3 x ^{3} + 6 x ^{2} - 12 x + 8}{x - 1}

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

Solution steps

\frac{x ^{4} - 3 x ^{3} + 6 x ^{2} - 12 x + 8}{x - 1}

Use the rational root theorem

= \frac{( x - 1 ) \frac{x ^{4} - 3 x ^{3} + 6 x ^{2} - 12 x + 8}{x - 1}}{x - 1}

\frac{x ^{4} - 3 x ^{3} + 6 x ^{2} - 12 x + 8}{x - 1} = x^{3} - 2 x^{2} + 4 x - 8

= \frac{( x - 1 ) ( x ^{3} - 2 x ^{2} + 4 x - 8 )}{x - 1}

Factor

x^{3} - 2 x^{2} + 4 x - 8 : (x - 2) (x^{2} + 4)

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

Cancel the common factor:

x - 1

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

(x - 3 + 4 i) (x - 3 - 4 i)

(- 4 + 7 i) + (- 4 - 7 i)

x y - 101 x^{2} + x^{2} - x^{2} y^{2} + 99 x y

3 x^{3} - 25 x^{2} + 58 x - 40

\frac{7}{53}

What is (x^4-3x^3+6x^2-12x+8)/(x-1) ?
The solution to (x^4-3x^3+6x^2-12x+8)/(x-1) is (x-2)(x^2+4)