How do you divide $(x^{3} + 6 x^{2} - 30 x + 102) \div (x + 10)$ $(x^3+6x^2-30x+102)div(x+10)$ using synthetic division?

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How do you divide $(x^{3} + 6 x^{2} - 30 x + 102) \div (x + 10)$ $(x^3+6x^2-30x+102)div(x+10)$ using synthetic division?

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Answer 1 · 2016-10-23T07:10:10

The result $\frac{x^{3} + 6 x^{2} - 30 x + 102}{x + 10} = (x^{2} - 4 x + 10) + \frac{2}{x + 10}$ $(x^3+6x^2-30x+102)/(x+10)=(x^2-4x+10)+2/(x+10)$

Explanation:

Let's do the division
$x^{3} + 6 x^{2} - 30 x + 102$ $x^3+6x^2-30x+102$ $a a a a a$ $color(white)(aaaaa)$ $∣ x + 10$ $∣x+10$
$x^{3} + 10 x^{2}$ $x^3+10x^2$ $a a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaaa)$ $∣ ∣ x^{2} - 4 x + 10$ $∣x^2-4x+10$
$0 - 4 x^{2} - 30 x$ $0- 4x^2-30x$
$a a$ $color(white)(aa)$ $- 4 x^{2} - 40 x$ $-4x^2-40x$
$a a a a a$ $color(white)(aaaaa)$ $0 + 10 x + 102$ $0+10x+102$
$a a a a a a a a a$ $color(white)(aaaaaaaaa)$ $10 x + 100$ $10x+100$
$a a a a a a a a a a a$ $color(white)(aaaaaaaaaaa)$ $0 + 2$ $0+2$

The remainder $= 2$ $=2$

so the result is $\frac{x^{3} + 6 x^{2} - 30 x + 102}{x + 10} = (x^{2} - 4 x + 10) + \frac{2}{x + 10}$ $(x^3+6x^2-30x+102)/(x+10)=(x^2-4x+10)+2/(x+10)$

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How do you divide $(x^{3} + 6 x^{2} - 30 x + 102) \div (x + 10)$ $(x^3+6x^2-30x+102)div(x+10)$ using synthetic division?

1 Answer

Explanation:

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How do you divide (x3+6x2−30x+102)÷(x+10)(x^3+6x^2-30x+102)div(x+10) using synthetic division?

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Explanation:

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How do you divide $(x^{3} + 6 x^{2} - 30 x + 102) \div (x + 10)$ $(x^3+6x^2-30x+102)div(x+10)$ using synthetic division?