Verify the division algorithm for divident = $2 x^{2} + 3 x + 1$ , divisor= $(x - 2)$ ,remainder $= 15$ ,quotient $= 2 x + 7$

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Solution

division algorithm
$d i v i d e n t = d i v i s o r \times q u o t i e n t + r e m a i n d e r$
so
$\begin{matrix} d i v i s e r \times q u o t i e n t + r e m a i n d e r = (x - 2) (2 x + 7) + 15 = 2 x^{2} - 4 x + 7 x - 14 + 15 = 2 x^{2} + 3 x + 1 = d i v i d e n t H e n c e v e r i f i e d \end{matrix}$

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