How do you divide $x^{3} + 7 x^{2} - 3 x + 4) \div (x + 2)$ $x^3+7x^2-3x+4) div(x+2)$ and identify any restrictions on the variable?

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How do you divide $x^{3} + 7 x^{2} - 3 x + 4) \div (x + 2)$ $x^3+7x^2-3x+4) div(x+2)$ and identify any restrictions on the variable?

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Answer 1 · 2017-12-20T14:02:54

$x^{2} + 5 x - 13 + \frac{30}{x + 2} \to (x \neq - 2)$ $x^2+5x-13+30/(x+2)to(x!=-2)$

Explanation:

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

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

$x^{2} (x + 2) - 2 x^{2} + 7 x^{2} - 3 x + 4$ $color(red)(x^2)(x+2)color(magenta)(-2x^2)+7x^2-3x+4$

$= x^{2} (x + 2) + 5 x (x + 2) - 10 x - 3 x + 4$ $=color(red)(x^2)(x+2)color(red)(+5x)(x+2)color(magenta)(-10x)-3x+4$

$= x^{2} (x + 2) + 5 x (x + 2) - 13 (x + 2) + 26 + 4$ $=color(red)(x^2)(x+2)color(red)(+5x)(x+2)color(red)(-13)(x+2)color(magenta)(+26)+4$

$= x^{2} (x + 2) + 5 x (x + 2) - 13 (x + 2) + 30$ $=color(red)(x^2)(x+2)color(red)(+5x)(x+2)color(red)(-13)(x+2)+30$

$quotient = x^{2} + 5 x - 13, remainder = 30$ $"quotient "=color(red)(x^2+5x-13)," remainder "=30$

$\Rightarrow \frac{x^{3} + 7 x^{2} - 3 x + 4}{x + 2}$ $rArr(x^3+7x^2-3x+4)/(x+2)$

$= x^{2} + 5 x - 13 + \frac{30}{x + 2} \to (x \neq - 2)$ $=x^2+5x-13+30/(x+2)to(x!=-2)$

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How do you divide $x^{3} + 7 x^{2} - 3 x + 4) \div (x + 2)$ $x^3+7x^2-3x+4) div(x+2)$ and identify any restrictions on the variable?

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How do you divide x3+7x2−3x+4)÷(x+2)x^3+7x^2-3x+4) div(x+2) and identify any restrictions on the variable?

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How do you divide $x^{3} + 7 x^{2} - 3 x + 4) \div (x + 2)$ $x^3+7x^2-3x+4) div(x+2)$ and identify any restrictions on the variable?