How do you solve $(x^{3} - 4 x^{2} - 11 x + 30) \div (x - 2) ?$ $(x^ { 3} - 4x ^ { 2} - 11x + 30 )\div (x - 2)?$

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How do you solve $(x^{3} - 4 x^{2} - 11 x + 30) \div (x - 2) ?$ $(x^ { 3} - 4x ^ { 2} - 11x + 30 )\div (x - 2)?$

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Answer 1 · 2018-01-29T10:07:52

$x^{2} - 2 x - 15$ $color(green)(x^2 -2x -15)$

Explanation:

$a a a a 2 a a ∣ a a 1 a a - 4 a a - 11 a a 30$ $color(white)(aaaa)2color(white)(aa)|color(white)(aa)1color(white)(aa)-4color(white)(aa)-11color(white)(aa)30$

$a a a a a a a a a a ↓ a a a a 2 a a - 4 - 30$ $color(white)(aaaaaaaaaa)darrcolor(white)(aaaa)2color(white)(aa)-4color(white)()-30$

$a a a a a a a - - - - - - - - -$ $color(white)(aaaaaaa)---------$

$a a a a a a a a a a a 1 a a - 2 a a - 15 a a 0$ $color(white)(aaaaaaaaaaa)1color(white)(aa)-2color(white)(aa)-15color(white)(aa)0$

$x^{2} - 2 x - 15$ $x^2 -2x -15$

Answer 2 · 2018-01-29T11:10:44

$x^{2} - 2 x - 15$ $x^2-2x-15$

Explanation:

$one way is to use the divisor as a factor in the numerator$ $"one way is to use the divisor as a factor in the numerator"$

$consider the numerator$ $"consider the numerator"$

$x^{2} (x - 2) + 2 x^{2} - 4 x^{2} - 11 x + 30$ $color(red)(x^2)(x-2)color(magenta)(+2x^2)-4x^2-11x+30$

$= x^{2} (x - 2) - 2 x (x - 2) - 4 x - 11 x + 30$ $=color(red)(x^2)(x-2)color(red)(-2x)(x-2)color(magenta)(-4x)-11x+30$

$= x^{2} (x - 2) - 2 x (x - 2) - 15 (x - 2) - 30 + 30$ $=color(red)(x^2)(x-2)color(red)(-2x)(x-2)color(red)(-15)(x-2)color(magenta)(-30)+30$

$= x^{2} (x - 2) - 2 x (x - 2) - 15 (x - 2) + 0$ $=color(red)(x^2)(x-2)color(red)(-2x)(x-2)color(red)(-15)(x-2)+0$

$quotient = x^{2} - 2 x - 15, remainder = 0$ $"quotient "=color(red)(x^2-2x-15)," remainder" =0$

$\Rightarrow \frac{x^{3} - 4 x^{2} - 11 x + 30}{x - 2} = x^{2} - 2 x - 15$ $rArr(x^3-4x^2-11x+30)/(x-2)=x^2-2x-15$

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How do you solve $(x^{3} - 4 x^{2} - 11 x + 30) \div (x - 2) ?$ $(x^ { 3} - 4x ^ { 2} - 11x + 30 )\div (x - 2)?$

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How do you solve $(x^{3} - 4 x^{2} - 11 x + 30) \div (x - 2) ?$ $(x^ { 3} - 4x ^ { 2} - 11x + 30 )\div (x - 2)?$