Factorise the expression and divide them as directed: (5p^2– 25p … - Vidyadip

Question

Factorise the expression and divide them as directed: $(5p^2– 25p + 20) \div (p – 1)$

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Answer

$(5p^2– 25p + 20) \div (p – 1)$
$ = \frac{{5({p^2} - 5p + 4)}}{{p - 1}}$
$ = \frac{{5({p^2} - p - 4p + 4)}}{{p - 1}}$. . . . [Applying Identity $IV]$
$ = \frac{{5\{ p(p - 1) - 4(p - 1)\} }}{{p - 1}}$
$ = \frac{{5(p - 1)(p - 4)}}{{p - 1}}$
$= 5 (p – 4)$

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