Write the polynomial $3 x^{2} - 5 x - 2$ as a product of two first degree polynomials.

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Solution

Given polynomial is $3 x^{2} - 5 x - 2$ .

By using the quadratic formula,
$\begin{matrix} x & = \frac{- (- 5) \pm \sqrt{25 + 24}}{6} = \frac{5 \pm \sqrt{49}}{6} = \frac{5 \pm 7}{6} = 2 or \frac{- 1}{3} \end{matrix}$

If $α$ and $β$ are roots of the equation $a x^{2} + b x + c = 0$ , then it can be rewritten as $a x^{2} + b x + c = a (x - α) (x - β)$ .

So, by using the above definition $3 x^{2} - 5 x - 2 = 3 (x - 2) (x + \frac{1}{3})$ .

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