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Factorisation by Regrouping Terms

If x + ax +...

Question

If $(x + a) (x + b) (x + c) = x^{3} - 10 x^{2} + 45 x - 15$ find $- (a + b + c)$ .

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Solution

$(x + a) (x + b) (x + c) = x^{3} - 10 x^{2} + 45 x - 15$
$= (x^{2} + (a + b) x + a b) (x + c)$
$= x^{3} + c x^{2} + (a + b) x^{2} + (a + b) c x + a b x + a b c$
$= x^{3} + x^{2} (a + b + c) + x (a c + b c + a b) + a b c$
on compairing $a + b + c = - 10$
$- (a + b + c) = 10$

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