Find the coefficient of $x^{2}$ & $x$ in the product of $(x - 5) (x + 3) (x + 7)$

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Solution

$(x - 5) (x + 3) (x + 7) = (x^{2} - 5 x + 3 x - 15) (x + 7)$

$= (x^{2} - 2 x - 15) (x + 7)$

$= x^{3} - 2 x^{2} - 15 x + 7 x^{2} - 14 x - 105$

$= x^{3} + 5 x^{2} - 29 x - 105$

Therefore, the coefficient of $x^{2}$ is $5$

and the coefficient of $x$ is $- 29$

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