How do you find the quotient of $\frac{m^{4} - 2 m^{3} + m^{2} + 12 m - 6}{m - 2}$ $(m^4-2m^3+m^2+12m-6)/(m-2)$ using synthetic division?

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How do you find the quotient of $\frac{m^{4} - 2 m^{3} + m^{2} + 12 m - 6}{m - 2}$ $(m^4-2m^3+m^2+12m-6)/(m-2)$ using synthetic division?

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Answer 1 · 2018-01-31T12:37:30

Quotient $Q = m^{2} + m + 14$ $color(green)(Q = m^2 + m + 14)$ , Remainder $R = \frac{22}{m - 2}$ $color(green)(R = 22 / (m-2))$

Explanation:

Synthetic Division :

$a a 2 a a ∣ a a 1 a a - 2 a a 1 a a 12 a a - 6$ $color(white)(aa)2color(white)(aa)|color(white)(aa)1color(white)(aa)-2color(white)(aa)1color(white)(aa)12color(white)(aa)-6$
$a a a a a ∣ a ⏐ ↓ a a a a 2 a a 0 a a a 2 a a a 28$ $color(white)(aaaaa)|color(white)(a)darrcolor(white)(aaaa)2color(white)(aa)0color(white)(aaa)2color(white)(aaa)28$
$a a a a a - - - - - - - - - -$ $color(white)(aaaaa)----------$
$a a a a a a a a a 1 a a a a 0 a a 1 a a a 14 a a a 22$ $color(white)(aaaaaaaaa)1color(white)(aaaa)0color(white)(aa)1color(white)(aaa)14color(white)(aaa)22$

Quotient $Q = m^{2} + m + 14$ $color(green)(Q = m^2 + m + 14)$ , Remainder $R = \frac{22}{m - 2}$ $color(green)(R = 22 / (m-2))$

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How do you find the quotient of $\frac{m^{4} - 2 m^{3} + m^{2} + 12 m - 6}{m - 2}$ $(m^4-2m^3+m^2+12m-6)/(m-2)$ using synthetic division?

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Explanation:

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How do you find the quotient of m4−2m3+m2+12m−6m−2(m^4-2m^3+m^2+12m-6)/(m-2) using synthetic division?

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How do you find the quotient of $\frac{m^{4} - 2 m^{3} + m^{2} + 12 m - 6}{m - 2}$ $(m^4-2m^3+m^2+12m-6)/(m-2)$ using synthetic division?