Answer :
The remainder when f(x) = 2x^4 + x^3- 8x - 1 is divided by x - 2 is 23
A polynomial is an expression consisting of the operations of addition, subtraction, multiplication of variables.
Polynomial based on degree is linear, quadratic, cubic.
The remainder theorem states that when a polynomial, f(x), is divided by a linear polynomial x - a, the remainder of is to f(a)
Given that f(x) = 2x⁴ + x³ - 8x - 1 is divided by x - 2
x - 2 = 0
x = 2
f(2) = 2(2)⁴ + (2)³ - 8(2) - 1 = 23
Hence The remainder when f(x) = 2x^4 + x^3- 8x - 1 is divided by x - 2 is 23
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By the remainder theorem, dividing [tex]f(x)[/tex] by [tex]x-2[/tex] leaves a remainder of [tex]f(2)[/tex], which is
[tex]f(2)=2(2)^4+(2)^3-8(2)-1=\boxed{23}[/tex]
which makes B the correct answer.
