Find the zeroes of the polynomial: $(3 x + 2) (x^{2} + 7 x - 60)$ .

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Solution

Consider the given polynomial.
$p (x) = (3 x + 2) (x^{2} + 7 x - 60)$

Zero of a polynomial $p (x)$ is the value of $x$ where $p (x) = 0$ .

$(3 x + 2) (x^{2} + 7 x - 60) = 0$
$3 x + 2 = 0$
$x = \frac{- 2}{3}$

And,
$x^{2} + 7 x - 60 = 0$
$x^{2} + 12 x - 5 x - 60 = 0$
$x (x + 12) - 5 (x + 12) = 0$
$(x - 5) (x + 12) = 0$
$x - 5 = 0$ or $x + 12 = 0$
$x = 5$ or $x = - 12$

Hence, zeroes of the given polynomial are $\frac{- 2}{3}, 5, - 12$ .

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