How do you long divide $\frac{x^{4} + x^{3} - 13 x^{2} - 25 x - 12}{x^{2} + 2 x + 1}$ $(x^4+x^3-13x^2-25x-12) / (x^2+2x+1)$ ?

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How do you long divide $\frac{x^{4} + x^{3} - 13 x^{2} - 25 x - 12}{x^{2} + 2 x + 1}$ $(x^4+x^3-13x^2-25x-12) / (x^2+2x+1)$ ?

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Answer 1 · 2016-12-10T10:45:16

The quotient is $= x^{2} - x - 12$ $=x^2-x-12$ and the remainder is $= 0$ $=0$

Explanation:

Let's do the long division

$a a a a$ $color(white)(aaaa)$ $x^{4} + x^{3} - 13 x^{2} - 25 x - 12$ $x^4+x^3-13x^2-25x-12$ $a a a a$ $color(white)(aaaa)$ $∣$ $∣$ $x^{2} + 2 x + 1$ $x^2+2x+1$

$a a a a$ $color(white)(aaaa)$ $x^{4} + 2 x^{3} + x^{2}$ $x^4+2x^3+x^2$ $a a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaaa)$ $∣$ $∣$ $x^{2} - x - 12$ $x^2-x-12$

$a a a a$ $color(white)(aaaa)$ $0 - x^{3} - 14 x^{2} - 25 x$ $0-x^3-14x^2-25x$

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

$a a a a a a a a a$ $color(white)(aaaaaaaaa)$ $0 - 12 x^{2} - 24 x - 12$ $0-12x^2-24x-12$

$a a a a a a a a a a a$ $color(white)(aaaaaaaaaaa)$ $- 12 x^{2} - 24 x - 12$ $-12x^2-24x-12$

$a a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaaa)$ $- 0 - 0 - 0$ $-0-0-0$

The quotient is $= x^{2} - x - 12$ $=x^2-x-12$ and the remainder is $= 0$ $=0$

Answer 2 · 2016-12-10T12:51:33

$x^{2} - x - 12$ $x^2-x-12$

Explanation:

$x^{4} + x^{3} - 13 x^{2} - 25 x - 12$ $" "x^4+x^3-13x^2-25x-12$
$color(red)(x^2)(x^2+2x+1) -> ul(x^4 +2x^3+x^2" " larr" subtract"$
$" "0 -x^3-14x^2-25x-12$
$color(red)(-x)(x^2+2x+1)->color(white)(.)ul(-x^3-2x^2color(white)(.)-x larr" subtract")$
$" "0-12x^2-24x-12$
$color(red)(-12)(x^2+2x+1)->" "color(white)(.)ul(-12x^2 -24x-12larr" subtract")$
$" "0" " +0" "+0$

There is no remainder

$(x^4+x^3-13x^2-25x-12)/(x^2+2x+1)" " =" " color(red)(x^2-x-12$

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How do you long divide $\frac{x^{4} + x^{3} - 13 x^{2} - 25 x - 12}{x^{2} + 2 x + 1}$ $(x^4+x^3-13x^2-25x-12) / (x^2+2x+1)$ ?

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How do you long divide (x^4+x^3-13x^2-25x-12) / (x^2+2x+1)x4+x3−13x2−25x−12x2+2x+1(x^4+x^3-13x^2-25x-12) / (x^2+2x+1)?

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How do you long divide $\frac{x^{4} + x^{3} - 13 x^{2} - 25 x - 12}{x^{2} + 2 x + 1}$ $(x^4+x^3-13x^2-25x-12) / (x^2+2x+1)$ ?