How do you find the quotient of $(2 - x + x^{2} - x^{3} - x^{4}) \div (x + 2)$ $(2-x+x^2-x^3-x^4)div(x+2)$ using synthetic division?

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How do you find the quotient of $(2 - x + x^{2} - x^{3} - x^{4}) \div (x + 2)$ $(2-x+x^2-x^3-x^4)div(x+2)$ using synthetic division?

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Answer 1 · 2018-06-29T16:10:36

The remainder is $0$ $0$ and the quotient is $= - x^{3} + x^{2} - x + 1$ $=-x^3+x^2-x+1$

Explanation:

Let's perform the synthetic division

$a a a a$ $color(white)(aaaa)$ $- 2$ $-2$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $- 1$ $-1$ $a a a a$ $color(white)(aaaa)$ $- 1$ $-1$ $a a a a a a$ $color(white)(aaaaaa)$ $1$ $1$ $a a a a$ $color(white)(aaaa)$ $- 1$ $-1$ $a a a a a a$ $color(white)(aaaaaa)$ $2$ $2$

$a a a a a a a$ $color(white)(aaaaaaa)$ #|color(white)(aaaa)##color(white)(aaaaaaaa)2# $a a a a a$ $color(white)(aaaaa)$ $- 2$ $-2$ $a a a a a$ $color(white)(aaaaa)$ $2$ $2$ $a a a a$ $color(white)(aaaa)$ $- 2$ $-2$

$a a a a a a a a a$ $color(white)(aaaaaaaaa)$ _________________________________________________________##

$a a a a a a a$ $color(white)(aaaaaaa)$ #|color(white)(aaaa)# $- 1$ $-1$ $a a a a a a$ $color(white)(aaaaaa)$ $1$ $1$ $a a a a$ $color(white)(aaaa)$ $- 1$ $-1$ $a a a a a$ $color(white)(aaaaa)$ $1$ $1$ $a a a a a a$ $color(white)(aaaaaa)$ $0$ $color(red)(0)$

The remainder is $0$ $0$ and the quotient is $= - x^{3} + x^{2} - x + 1$ $=-x^3+x^2-x+1$

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How do you find the quotient of $(2 - x + x^{2} - x^{3} - x^{4}) \div (x + 2)$ $(2-x+x^2-x^3-x^4)div(x+2)$ using synthetic division?

1 Answer

Explanation:

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How do you find the quotient of (2−x+x2−x3−x4)÷(x+2)(2-x+x^2-x^3-x^4)div(x+2) using synthetic division?

1 Answer

Explanation:

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How do you find the quotient of $(2 - x + x^{2} - x^{3} - x^{4}) \div (x + 2)$ $(2-x+x^2-x^3-x^4)div(x+2)$ using synthetic division?