Divide $p (x)$ by $g (x)$ in the following case and verify division algorithm.
$p (x) = 2 x^{2} - 9 x + 9; g (x) = x - 3$

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Solution

The division of $p (x) = 2 x^{2} - 9 x + 9$ by $g (x) = x - 3$ is as shown above:

Now we know that the division algorithm states that:
Dividend $= ($ Divisor $\times$ quotient $) +$ Remainder

Here, the dividend is $2 x^{2} - 9 x + 9$ , the divisor is $x - 3$ , the quotient is $2 x - 3$ and the remainder is $0$ , therefore,

$2 x^{2} - 9 x + 9 = [(x - 3) (2 x - 3)] + 0 \Rightarrow 2 x^{2} - 9 x + 9 = [x (2 x - 3) - 3 (2 x - 3)] \Rightarrow 2 x^{2} - 9 x + 9 = x^{2} - 3 x - 6 x + 9 \Rightarrow 2 x^{2} - 9 x + 9 = 2 x^{2} - 9 x + 9$

Hence, the division algorithm is verified.

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