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Division of a Polynomial by a Monomial

Divide 15 x...

Question

Divide $15 x^{3} - 20 x^{2} + 13 x - 12 by 3 x - 6$ and verify that Dividend $=$ Divisor $\times$ Quotient + Remainder.

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Solution

$3 x - 6) 15 x^{3} - 20 x^{2} + 13 x - 12 (5 x^{2} + \frac{10}{3} x + 11$
$15 x^{3} - 30 x^{2}$
_________ Dividend $= 15 x^{3} - 20 x^{2} + 13 x - 12$
$10 x^{2} + 13 x - 12$
$10 x^{2} - 20 x$
_ Quotient $\times$ Divisors $= (3 x - 6) (5 x^{2} + \frac{10}{3} x + 11)$
$33 x - 12$
$33 x - 66$ $= 15 x^{3} + 10 x^{2} + 33 x - 30 x^{2} - 20 x - 66$
$= 15 x^{3} - 20 x^{2} + 13 x - 66$
$54$ Remainder $= 54$
______
Quotient $\times$ Divisor $+$ remainder $= 15 x^{3} - 20 x^{2} + 13 x - 66 + 54$
$= 15 x^{3} - 20 x^{2} + 13 x - 12$ which is dividend.

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