What is (x^5+12x^2-5x)/(x^2-2x+5) ?

The solution to (x^5+12x^2-5x)/(x^2-2x+5) is x(x^2+2x-1)

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simplify (x^5+12x^2-5x)/(x^2-2x+5)

simplify

\frac{x ^{5} + 12 x ^{2} - 5 x}{x ^{2} - 2 x + 5}

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

Solution steps

\frac{x ^{5} + 12 x ^{2} - 5 x}{x ^{2} - 2 x + 5}

Factor

x^{5} + 12 x^{2} - 5 x : x (x^{4} + 12 x - 5)

= \frac{x ( x ^{4} + 12 x - 5 )}{x ^{2} - 2 x + 5}

Factor

x^{4} + 12 x - 5 : (x^{2} + 2 x - 1) (x^{2} - 2 x + 5)

= \frac{x ( x ^{2} + 2 x - 1 ) ( x ^{2} - 2 x + 5 )}{x ^{2} - 2 x + 5}

Cancel the common factor:

x^{2} - 2 x + 5

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

100 \div 20

(x - 2) (x + 8)

(5 x) (- 3 x)

(2 - 3 x)^{2}

72 x^{3}

What is (x^5+12x^2-5x)/(x^2-2x+5) ?
The solution to (x^5+12x^2-5x)/(x^2-2x+5) is x(x^2+2x-1)