How do you divide $(5 x^{4} - 3 x^{3} + 2 x^{2} - 1) \div (x^{2} + 4)$ $(5x^4-3x^3+2x^2-1)div(x^2+4)$ using long division?

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How do you divide $(5 x^{4} - 3 x^{3} + 2 x^{2} - 1) \div (x^{2} + 4)$ $(5x^4-3x^3+2x^2-1)div(x^2+4)$ using long division?

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Answer 1 · 2017-02-03T08:01:49

The answer is $= (5 x^{2} - 3 x - 18) + \frac{12 x + 71}{x^{2} + 4}$ $=(5x^2-3x-18)+(12x+71)/(x^2+4)$

Explanation:

Let's do the long division

$a a a a$ $color(white)(aaaa)$ $5 x^{4} - 3 x^{3} + 2 x^{2} - 1$ $5x^4-3x^3+2x^2-1$ $a a a a a a a a$ $color(white)(aaaaaaaa)$ $∣$ $|$ $x^{2} + 4$ $x^2+4$

$a a a a$ $color(white)(aaaa)$ $5 x^{4}$ $5x^4$ $a a a a a a$ $color(white)(aa aaaa)$ $+ 20 x^{2}$ $+20x^2$ $a a a a a a a a a a a$ $color(white)(aaaaaaaaaaa)$ $∣$ $|$ $5 x^{2} - 3 x - 18$ $5x^2-3x-18$

$a a a a$ $color(white)(aaaa)$ $0 - 3 x^{3}$ $0-3x^3$ $a a a$ $color(white)(aa a)$ $- 18 x^{2}$ $-18x^2$ $a a a a a a a$ $color(white)(aaaaaaa)$

$a a a a a a$ $color(white)(aaaaaa)$ $- 3 x^{3}$ $-3x^3$ $a a a a$ $color(white)(aaaa)$ $- 18 x^{2} - 12 x - 1$ $-18x^2-12x-1$ $a a a a a a a$ $color(white)(aaaaaaa)$

$a a a a a a a a$ $color(white)(aaaaaaaa)$ $0$ $0$ $a a a a a$ $color(white)(aaaaa)$ $- 18 x^{2} - 12 x$ $-18x^2-12x$ $a$ $color(white)(a)$ $- 72$ $-72$

$a a a a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaaaaa)$ $0$ $0$ $a a a$ $color(white)(aaa)$ $+ 12 x$ $+12x$ $a a$ $color(white)(aa)$ $+ 71$ $+71$

Therefore,

$\frac{5 x^{4} - 3 x^{3} + 2 x^{2} - 1}{x^{2} + 4} = 5 x^{2} - 3 x - 18 + \frac{12 x + 71}{x^{2} + 4}$ $(5x^4-3x^3+2x^2-1)/(x^2+4)=5x^2-3x-18+(12x+71)/(x^2+4)$

The quotient is $= 5 x^{2} - 3 x - 18$ $=5x^2-3x-18$

The remainder is $= 12 x + 71$ $=12x+71$

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How do you divide $(5 x^{4} - 3 x^{3} + 2 x^{2} - 1) \div (x^{2} + 4)$ $(5x^4-3x^3+2x^2-1)div(x^2+4)$ using long division?

1 Answer

Explanation:

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Explanation:

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How do you divide $(5 x^{4} - 3 x^{3} + 2 x^{2} - 1) \div (x^{2} + 4)$ $(5x^4-3x^3+2x^2-1)div(x^2+4)$ using long division?