How do you divide $\frac{x^{2} - 5 x + 4}{x - 2}$ $(x^2 - 5x + 4)/( x-2)$ ?

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How do you divide $\frac{x^{2} - 5 x + 4}{x - 2}$ $(x^2 - 5x + 4)/( x-2)$ ?

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Answer 1 · 2017-05-23T13:20:12

$x - 3 - \frac{2}{x - 2}$ $x-3-2/(x-2)$

Explanation:

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

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

$x (x - 2) + 2 x - 5 x + 4$ $color(red)(x)(x-2)color(magenta)(+2x)-5x+4$

$= x (x - 2) - 3 (x - 2) - 6 + 4$ $=color(red)(x)(x-2)color(red)(-3)(x-2)color(magenta)(-6)+4$

$= x (x - 2) - 3 (x - 2) - 2$ $=color(red)(x)(x-2)color(red)(-3)(x-2)-2$

$quotient = x - 3, remainder = - 2$ $"quotient " =color(red)(x-3)," remainder "= -2$

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

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How do you divide $\frac{x^{2} - 5 x + 4}{x - 2}$ $(x^2 - 5x + 4)/( x-2)$ ?

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How do you divide $\frac{x^{2} - 5 x + 4}{x - 2}$ $(x^2 - 5x + 4)/( x-2)$ ?