Divide $(5 x^{2} - 25 x + 20)$ by $(x - 1)$ .

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Solution

$(5 x^{2} - 25 x + 20) \div (x - 1)$
$= 5 (x^{2} - 5 x + 4) \div (x - 1)$
This can be solved in two ways.
Method $1$ :
Division (Refer image .1)
Quotient $= x - 4$
Ans: $(x - 4) \times 5 = 5 x - 20$
Method $2$ :-
$\frac{5 x^{2} - 25 x + 20}{x - 1} = \frac{5 (x^{2} - 5 x + 4)}{(x - 1)}$
$= \frac{5 (x^{2} - 4 x - x + 4)}{(x - 1)}$
$= \frac{5 (x - 4) x - 1 (x - 4)}{(x - 1)}$
$= \frac{5 (x - 4) (x - 1)}{(x - 1)}$
$= 5 (x - 4) = 5 x - 20$

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