How do you divide $(y^{4} - 8 y^{3} + 10 y^{2} + 2 y + 4) \div (y - 2)$ $(y^4-8y^3+10y^2+2y+4)div(y-2)$ using synthetic division?

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How do you divide $(y^{4} - 8 y^{3} + 10 y^{2} + 2 y + 4) \div (y - 2)$ $(y^4-8y^3+10y^2+2y+4)div(y-2)$ using synthetic division?

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Answer 1 · 2017-07-26T06:24:46

The remainder is $0$ $color(red)(0)$ and the quotient is $= y^{3} - 6 y^{2} - 2 y - 2$ $=y^3-6y^2-2y-2$

Explanation:

Let's perform the [synthetic division]

$a a a a$ $color(white)(aaaa)$ $2$ $2$ $a a a a a a$ $color(white)(aaaaaa)$ $∣$ $|$ $a a$ $color(white)(aa)$ $1$ $1$ $a a a a$ $color(white)(aaaa)$ $- 8$ $-8$ $a a a a a a$ $color(white)(aaaaaa)$ $10$ $10$ $a a a a a a a$ $color(white)(aaaaaaa)$ $2$ $2$ $a a a a a a a$ $color(white)(aaaaaaa)$ $4$ $4$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ _________

$a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $a a a a a$ $color(white)(aaaaa)$ $2$ $2$ $a a a a$ $color(white)(aaaa)$ $- 12$ $-12$ $a a a a a$ $color(white)(aaaaa)$ $- 4$ $-4$ $a a a a a a$ $color(white)(aaaaaa)$ $- 4$ $-4$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ ________

$a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a$ $color(white)(aaa)$ $1$ $1$ $a a a$ $color(white)(aaa)$ $- 6$ $-6$ $a a a a a$ $color(white)(aaaaa)$ $- 2$ $-2$ $a a a a a a$ $color(white)(aaaaaa)$ $- 2$ $-2$ $a a a a a a a$ $color(white)(aaaaaaa)$ $0$ $color(red)(0)$

The remainder is $0$ $color(red)(0)$ and the quotient is $= y^{3} - 6 y^{2} - 2 y - 2$ $=y^3-6y^2-2y-2$

$\frac{y^{4} - 8 y^{3} + 10 y^{2} + 2 y + 4}{y - 2} = y^{3} - 6 y^{2} - 2 y - 2$ $(y^4-8y^3+10y^2+2y+4)/(y-2)=y^3-6y^2-2y-2$

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How do you divide $(y^{4} - 8 y^{3} + 10 y^{2} + 2 y + 4) \div (y - 2)$ $(y^4-8y^3+10y^2+2y+4)div(y-2)$ using synthetic division?

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Explanation:

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How do you divide (y^4-8y^3+10y^2+2y+4)div(y-2)(y4−8y3+10y2+2y+4)÷(y−2)(y^4-8y^3+10y^2+2y+4)div(y-2) using synthetic division?

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Explanation:

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How do you divide $(y^{4} - 8 y^{3} + 10 y^{2} + 2 y + 4) \div (y - 2)$ $(y^4-8y^3+10y^2+2y+4)div(y-2)$ using synthetic division?