Solve the following quadratic equation by factorization method: $3 x^{2} - 23 x + 40 = 0$ .

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Solution

$3 x^{2} - 23 x + 40 = 0$
$3 x^{2} - 15 x - 8 x + 40 = 0$ , split the middle term

$(3 x^{2} - 15 x) + (- 8 x + 40)$ group the terms
$3 x (x - 5) - 8 (x - 5) = 0$
$(x - 5) (3 x - 8) = 0$ , factor
$x - 5 = 0$ or $3 x - 8 = 0$ , zero product property
$x = 5$ or $x = \frac{8}{3}$

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