Any polynomial can be written as : p( x ) =q( x ) + r( x ) #160; b( x ) #160; .....1 there, p( x ) = a( x ) #160; b( x ) #160; = x ^ 3 + x ^ ...

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Division of a Polynomial by a Monomial

x3+x2+2x-12x-...

Question

$\frac{x^{3} + x^{2} + 2 x - 12}{x - 3}$

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Solution

Any polynomial can be written as :
$p (x) = q (x) + \frac{r (x)}{b (x)} . . . . .1$
there, $p (x) = \frac{a (x)}{b (x)} = \frac{x^{3} + x^{2} + 2 x - 12}{x - 3}$
$∴ p (x) = \frac{x^{2} (x - 3) + 4 x (x - 3) + 14 (x - 3) + 30}{x - 3}$
$p (x) = x^{2} + 4 x + 14 + \frac{30}{x - 3} . . . . .2$
From $1$ and $2$ ;
$q (x) = x^{2} + 4 x + 14$
$r (x) = 30$
Answer: The given polynomial gives the quotient as $(x^{2} + 4 x + 14)$ and remainder as $30$ .

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