Find the quotient and the remainder when $10 - 4 x + 3 x^{2}$ is divided by $x - 2$ .

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Solution

Let us first write the terms of each polynomial in descending order ( or ascending order). thus, the given problem becomes $93 x^{2} - 4 x + 10) \div (x - 2)$
(i) $\frac{3 x^{2}}{x} = 3 x$
(ii) $3 x (x - 2) = 3 x^{2} - 6 x$
(iii) $\frac{2 x}{2} = 2$
(iv) $2 (x - 2) = 2 x - 4$
$∴$ Quotient $= 3 x + 2$ and Remainders=14
$(i . e . 3 x^{2} - 4 x + 10 = (x - 2) (3 x + 2) + 14$ and is in form
$D i v i d e d = (D i v i s o r \times q u o t i e n t + R e m a i n d e r)$

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