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Answer :
The remainder when the polynomial 2x⁴ + x³ - 8x - 1 is divided by x - 2 is 23, as calculated by substituting x with 2 in the polynomial according to the Remainder Theorem.
To find the remainder when f(x) = 2x⁴ + x³ - 8x - 1 is divided by x - 2, we can use the synthetic division or the Remainder Theorem. According to the Remainder Theorem, if a polynomial f(x) is divided by x - a, the remainder is f(a). In this case, we substitute x with 2 in the polynomial f(x).
Thus, substituting 2 into f(x) we get:
f(2) = 2(2)⁴ + (2)³ - 8(2) - 1
f(2) = 2(16) + 8 - 16 - 1
f(2) = 32 + 8 - 16 - 1
f(2) = 40 - 16 - 1
f(2) = 24 - 1
f(2) = 23.
Therefore, the remainder when f(x) is divided by x - 2 is 23.
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Answer:
B.23
Step-by-step explanation:
By the remainder theorem, the remainder is going to be f(2).
That is equal to 2*2^4+2^3-8*2-1=23
I hope this helped you.
