How do you divide $(5 x^{4} + 14 x^{3} + 9 x) \div (x^{2} + 3 x)$ $(5x^4+14x^3+9x)div(x^2+3x)$ using long division?

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Answer 1 · 2016-11-14T15:16:20

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

Let's do the long division

$a a a a$ $color(white)(aaaa)$ $5 x^{4} + 14 x^{3} + 9 x$ $5x^4+14x^3+9x$ $a a a a$ $color(white)(aaaa)$ $∣$ $∣$ $x^{2} + 3 x$ $x^2+3x$

$a a a a$ $color(white)(aaaa)$ $5 x^{4} + 15 x^{3}$ $5x^4+15x^3$ $a a a a a a a a a$ $color(white)(aaaaaaaaa)$ $∣$ $∣$ $5 x^{2} - x + 3$ $5x^2-x+3$

$a a a a a a$ $color(white)(aaaaaa)$ $0 - x^{3}$ $0-x^3$

$a a a a a a a a$ $color(white)(aaaaaaaa)$ $- x^{3} - 3 x^{2}$ $-x^3-3x^2$

$a a a a a a a a a a$ $color(white)(aaaaaaaaaa)$ $0 + 3 x^{2} + 9 x$ $0+3x^2+9x$

$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ $+ 3 x^{2} + 9 x$ $+3x^2+9x$

$a a a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaaaa)$ $0 + 0$ $0+0$

$\frac{5 x^{4} + 14 x^{3} + 9 x}{x^{2} + 3 x} = 5 x^{2} - x + 3$ $(5x^4+14x^3+9x)/(x^2+3x)=5x^2-x+3$

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

How do you divide (5x^4+14x^3+9x)div(x^2+3x)(5x4+14x3+9x)÷(x2+3x)(5x^4+14x^3+9x)div(x^2+3x) using long division?