Find the quotient and remainder using synthetic division.
$(2 x^{4} - 7 x^{3} - 13 x^{2} + 63 x - 48) \div (2 x - 1)$

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Solution

We divide the polynomial $2 x^{4} - 7 x^{3} - 13 x^{2} + 63 x - 48$ by $2 x - 1$ as shown in the above image:

From the above division, we conclude that the quotient is $x^{3} - 3 x^{2} - 8 x + \frac{55}{2}$ and the remainder is $- \frac{41}{2}$ .

Hence, the quotient is $x^{3} - 3 x^{2} - 8 x + \frac{55}{2}$ and the remainder is $- \frac{41}{2}$ .

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