How do you divide $\frac{2 x^{3} - 5 x^{2} + 22 x}{2 x + 3}$ $( 2x^3-5x^2+22x)/(2x +3)$ ?

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How do you divide $\frac{2 x^{3} - 5 x^{2} + 22 x}{2 x + 3}$ $( 2x^3-5x^2+22x)/(2x +3)$ ?

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Answer 1 · 2018-03-29T14:28:37

$x^{2} - 4 x + 17 - \frac{51}{2 x + 3}$ $x^2-4x+17-51/(2x+3)$

Explanation:

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

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

$x^{2} (2 x + 3) - 3 x^{2} - 5 x^{2} + 22 x$ $color(red)(x^2)(2x+3)color(magenta)(-3x^2)-5x^2+22x$

$= x^{2} (2 x + 3) - 4 x (2 x + 3) + 12 x + 22 x$ $=color(red)(x^2)(2x+3)color(red)(-4x)(2x+3)color(magenta)(+12x)+22x$

$= x^{2} (2 x + 3) - 4 x (2 x + 3) + 17 (2 x + 3) - 51$ $=color(red)(x^2)(2x+3)color(red)(-4x)(2x+3)color(red)(+17)(2x+3)color(magenta)(-51)$

$quotient = x^{2} - 4 x + 17, remainder = - 51$ $"quotient "=color(red)(x^2-4x+17)," remainder "=-51$

$\Rightarrow \frac{2 x^{3} - 5 x^{2} + 22 x}{2 x + 3}$ $rArr(2x^3-5x^2+22x)/(2x+3)$

$= x^{2} - 4 x + 17 - \frac{51}{2 x + 3}$ $=x^2-4x+17-51/(2x+3)$

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How do you divide $\frac{2 x^{3} - 5 x^{2} + 22 x}{2 x + 3}$ $( 2x^3-5x^2+22x)/(2x +3)$ ?

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How do you divide 2x3−5x2+22x2x+3( 2x^3-5x^2+22x)/(2x +3)?

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How do you divide $\frac{2 x^{3} - 5 x^{2} + 22 x}{2 x + 3}$ $( 2x^3-5x^2+22x)/(2x +3)$ ?