Divide $p (x) = 2 x^{3} - 11 x^{2} + 19 x - 10$ by g(x) = 2x - 5. Find the quotient and remainder.

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Solution

Given,
$p (x) = 2 x^{3} - 11 x^{2} + 19 x - 10$
$g (x) = 2 x - 5$
$x^{2} - 3 x + 2 - ------------------------- -$
$2 x - 5) 2 x^{3} - 11 x^{2} + 19 x - 10$
$2 x^{3} - 5 x^{2}$
$(-)$ $(+)$
____
$- 6 x^{2} + 19 x$
$- 6 x^{2} + 15 x$
$(+)$ $(-)$

$+ 4 x - 10$
$+ 4 x - 10$
$(-)$ $(+)$
_
$0$

$\Rightarrow 2 x^{3} - 11 x^{2} + 19 x - 10 = (2 x - 5) (x^{2} - 3 x + 2)$

$∴$ Quotient $= x^{2} - 3 x + 2$ and remainder $= 0$ .

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