Divide using the long division method and check the answer.
$- 11 x + 5 x - 4$ by $2 x - 1$

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Solution

We divide $- 11 x^{2} + 5 x - 4$ by $(2 x - 1)$ as shown in the above image:

From the division, we observe that the quotient is $- \frac{11}{2} x - \frac{1}{4}$ and the remainder is $- \frac{17}{4}$ .

We know that the division algorithm states that:
Dividend $=$ Divisor $\times$ Quotient $+$ Remainder

We apply the division algorithm to check the answer as follows:

$D i v i d e n d = D i v i s o r \times Q u o t i e n t + R e m a i n d e r - 11 x^{2} + 5 x - 4 = [(2 x - 1) (- \frac{11}{2} x - \frac{1}{4})] - \frac{17}{4} - 11 x^{2} + 5 x - 4 = - 11 x^{2} - \frac{1}{2} x + \frac{11}{2} x + \frac{1}{4} - \frac{17}{4} - 11 x^{2} + 5 x - 4 = - 11 x^{2} + \frac{10}{2} x - \frac{16}{4} - 11 x^{2} + 5 x - 4 = - 11 x^{2} + 5 x - 4 H e n c e v e r i f i e d .$

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