The remainder when x³ + 3x² + 3x + 1 is divided by x + 1 is 0.
What is Remainder theorem?
The polynomial remainder theorem, also known as little Bézout's theorem, is an algebraic application of Euclidean polynomial division. It says that f is equal to the remainder of dividing a polynomial f(x) by a linear polynomial (x-r) is f(r).
Given: [tex]f(x) = x^3 + 3x^3 + 3x + 1[/tex]
We have to find the remainder of polynomial f(x) when divided by (x + 1).
By using the Remainder theorem, the remainder of f(x) when divided by
(x - r) is f(r).
Here we have to find the value of f(-1).
Plug x = -1 is given polynomial f(x).
[tex]f(-1) = (-1)^3 + 3(-1)^2 +3(-1)+1 \\f(-1) = -1 + 3 - 3 + 1\\f(-1) = 0[/tex]
Hence, the remainder when x³ + 3x² + 3x + 1 is divided by x + 1 is 0.
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