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Remainder Theorem

If 3 is a zer...

Question

If 3 is a zero of the polynomial $p (x) = a x - 6$ . What is the remainder when $p (x)$ is divided by $x - 5 ?$

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Solution

The correct option is B 4
Given, 3 is a zero of the polynomial.
$\Rightarrow$ $p (3) = 0$
$\Rightarrow$ $a (3) - 6 = 0$
$\Rightarrow$ $3 a = 6$
$\Rightarrow$ $a = 2$

$∴$ $p (x) = 2 x - 6$
From remainder theorem, we have
The remainder = $p (5)$
$\Rightarrow 2 (5) - 6$
$\Rightarrow 4$

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