Show that -1 is a zero of the polynomial $2 x^{3} - x^{2} + x + 4$ .

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Solution

Let the given polynomial be $p (x) = 2 x^{3} - x^{2} + x + 4$ .
We know that, $x = a$ is a zero of a polynomial, $f (x)$ , if and only if $f (a) = 0$ .

Now, $p (- 1) = 2 (- 1)^{3} - (- 1)^{2} + (- 1) + 4$
$= - 2 - 1 - 1 + 4$
$= 0$
Here, $p (- 1) = 0$
Hence, $- 1$ is a zero of the polynomial $2 x^{3} - x^{2} + x + 4$ .

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