Question 5(iii)
Factorise the expressions and divide them as directed
$(5 p^{2} - 25 p + 20) \div (p - 1)$

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Solution

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

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