How do you divide $\frac{x^{3} - 10 x^{2} + 30 x + 3}{x - 5}$ $(x^3-10x^2+30x+3)/(x-5)$ ?

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How do you divide $\frac{x^{3} - 10 x^{2} + 30 x + 3}{x - 5}$ $(x^3-10x^2+30x+3)/(x-5)$ ?

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Answer 1 · 2015-11-14T16:22:32

Use long division or synthetic division.

Explanation:

![http://calc101.com/webMathematica/ long-divide.jsp

First step: Realize that $x$ $x$ needs to be multiplied by $x^{2}$ $x^2$ in order to be the $x^{3}$ $x^3$ in $x^{3} - 10 x^{2} + 30 x + 3$ $x^3-10x^2+30x+3$ . Then, multiply the $x^{2}$ $x^2$ throughout $x - 5$ $x-5$ to get $x^{3} - 5 x^{2}$ $x^3-5x^2$ and SUBTRACT it (remember, the signs will change) from $x^{3} - 10 x^{2} + 30 x + 3$ $x^3-10x^2+30x+3$ .

You are left with $- 5 x^{2} + 30 x + 3$ $-5x^2+30x+3$ , but only the first term is important for now. Like you did with the $x^{3}$ $x^3$ in the first step, realize that you will need to add a $- 5 x$ $-5x$ on top so that the $x (- 5 x) = - 5 x^{2}$ $x(-5x)=-5x^2$ . Continue multiplying and subtracting until you get to 28, which is the remainder.

All together, the answer would be written as:
$x^{2} - 5 x + 5 + \frac{28}{x - 5}$ $color(blue)(x^2-5x+5+28/(x-5)$

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How do you divide $\frac{x^{3} - 10 x^{2} + 30 x + 3}{x - 5}$ $(x^3-10x^2+30x+3)/(x-5)$ ?

1 Answer

Explanation:

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How do you divide (x^3-10x^2+30x+3)/(x-5)x3−10x2+30x+3x−5(x^3-10x^2+30x+3)/(x-5)?

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How do you divide $\frac{x^{3} - 10 x^{2} + 30 x + 3}{x - 5}$ $(x^3-10x^2+30x+3)/(x-5)$ ?