What is expand (x^4-5x^3+6x^2+4x-8)/(x+1) ?

The solution to expand (x^4-5x^3+6x^2+4x-8)/(x+1) is x^3-6x^2+12x-8

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expand (x^4-5x^3+6x^2+4x-8)/(x+1)

expand

\frac{x ^{4} - 5 x ^{3} + 6 x ^{2} + 4 x - 8}{x + 1}

x^{3} - 6 x^{2} + 12 x - 8

Solution steps

\frac{x ^{4} - 5 x ^{3} + 6 x ^{2} + 4 x - 8}{x + 1}

Factor

x^{4} - 5 x^{3} + 6 x^{2} + 4 x - 8 : (x + 1) (x - 2)^{3}

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

Cancel the common factor:

x + 1

= (x - 2)^{3}

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

a = x, b = 2

= x^{3} - 3 x^{2} \cdot 2 + 3 x \cdot 2^{2} - 2^{3}

Simplify

x^{3} - 3 x^{2} \cdot 2 + 3 x \cdot 2^{2} - 2^{3} : x^{3} - 6 x^{2} + 12 x - 8

= x^{3} - 6 x^{2} + 12 x - 8

\frac{11 ( x ^{2} + 2 3 x y + 3 y ^{2} )}{4}

\frac{s + 3}{( s + 1 ) ( s ^{2} + 2 s + 3 )}

(2 x + y cos (x y)) d x + x cos (x y) d y

\frac{6400 - 1600 π}{8 ( 8 + 2 π ) ^{2}}

(x, y, z) - \frac{( - 5 x - 5 y + 5 z )}{5 3} (- 5 - 5 + 5)

What is expand (x^4-5x^3+6x^2+4x-8)/(x+1) ?
The solution to expand (x^4-5x^3+6x^2+4x-8)/(x+1) is x^3-6x^2+12x-8