Find the quotient and remainder on dividing $p (x)$ by $g (x)$ in the following case, without actual division.
$p (x) = x^{2} + 7 x + 10; g (x) = x - 2$

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Solution

It is given that the dividend is $p (x) = x^{2} + 7 x + 10$ , the divisor is $g (x) = x - 2$ , therefore, the division is as shown above.

Hence, from the division, we get that the quotient is $x + 9$ and the remainder is $28$ .

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Question 1 (i)
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

$p (x) = x^{3} - 3 x^{2} + 5 x - 3, g (x) = x^{2} - 2$