How do you divide $(n^{4} + 5 n^{3} - 6 n + 3) \div (n + 3)$ $(n^4+5n^3-6n+3)div(n+3)$ using synthetic division?

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How do you divide $(n^{4} + 5 n^{3} - 6 n + 3) \div (n + 3)$ $(n^4+5n^3-6n+3)div(n+3)$ using synthetic division?

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Answer 1 · 2017-05-30T05:36:44

The remainder is $= - 33$ $=-33$ and the quotient is $= n^{3} + 2 n^{2} - 6 n + 12$ $=n^3+2n^2-6n+12$

Explanation:

Let's perform the synthetic division

$a a a a$ $color(white)(aaaa)$ $- 3$ $-3$ $a a a a a$ $color(white)(aaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $1$ $1$ $a a a a a a$ $color(white)(aaaaaa)$ $5$ $5$ $a a a a a a$ $color(white)(aaaaaa)$ $0$ $0$ $a a a a a$ $color(white)(aaaaa)$ $- 6$ $-6$ $a a a a a a a$ $color(white)(aaaaaaa)$ $3$ $3$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ _________

$a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $a a a a a a$ $color(white)(aaaaaa)$ $- 3$ $-3$ $a a a a a a$ $color(white)(aaaaaa)$ $- 6$ $-6$ $a a a a$ $color(white)(aaaa)$ $18$ $18$ $a a a a a$ $color(white)(aaaaa)$ $- 36$ $-36$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ ________

$a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $1$ $1$ $a a a a a a a$ $color(white)(aaaaaaa)$ $2$ $2$ $a a a a a a$ $color(white)(aaaaaa)$ $- 6$ $-6$ $a a a a$ $color(white)(aaaa)$ $12$ $12$ $a a a a a$ $color(white)(aaaaa)$ $- 33$ $color(red)(-33)$

$\frac{n^{4} + 5 n^{3} - 6 n + 3}{n + 3} = (n^{3} + 2 n^{2} - 6 n + 12) - \frac{33}{n + 3}$ $(n^4+5n^3-6n+3)/(n+3)=(n^3+2n^2-6n+12)-33/(n+3)$

The remainder is $= - 33$ $=-33$ and the quotient is $= n^{3} + 2 n^{2} - 6 n + 12$ $=n^3+2n^2-6n+12$

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How do you divide $(n^{4} + 5 n^{3} - 6 n + 3) \div (n + 3)$ $(n^4+5n^3-6n+3)div(n+3)$ using synthetic division?

1 Answer

Explanation:

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How do you divide (n4+5n3−6n+3)÷(n+3)(n^4+5n^3-6n+3)div(n+3) using synthetic division?

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How do you divide $(n^{4} + 5 n^{3} - 6 n + 3) \div (n + 3)$ $(n^4+5n^3-6n+3)div(n+3)$ using synthetic division?