Answer :
Final answer:
The remainder when dividing f(x) = 2x⁴ + x³ - 8x - 1 by x - 2 is 23(option B).. This is found using synthetic division.
Explanation:
The remainder when dividing f(x) = 2x⁴ + x³ - 8x - 1 by x - 2 can be found using synthetic division or polynomial division.
- Arrange the terms of the polynomial in descending order of powers.
- Write the constant term outside the synthetic division box.
- Bring down the leading coefficient, which is 2.
- Multiply the divisor x - 2 by the result from step 3 and place the product below the next term.
- Add the terms in the second row and write the sum beneath the next term.
- Repeat steps 4 and 5 until all terms have been added.
The remainder is the value in the bottom right corner of the synthetic division box. In this case, the remainder is 23 (B).
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