Divide $2 x^{2} + x - 15$ by $x + 3$ and verify the division algorithm.

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Solution

First, we will write the given polynomials in their standard forms in decreasing order of degree's and then perform the division as shown below:

$∴$ Quotient $= (2 x - 5)$ and Remainder $= 0$
Division Algorithm says,
$\Rightarrow$ (Quotient $\times$ Divisor $+$ Remainder)
$= (2 x - 5) (x + 3) + 0 = 2 x^{2} - 5 x + 6 x - 15 = 2 x^{2} + x - 15$
$=$ Dividend
Thus, (Quotient $\times$ Divisor $) +$ Remainder $=$ Dividend
Hence, the division algorithm is verified.

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