The remainder when x² + 2x + 1 is divided by x + 1 is 0.
Given,
The polynomial functions; x² + 2x + 1 and x + 1
We have to find the remainder when x² + 2x + 1 is divided by x + 1
Remainder theorem;-
Remainder Theorem is a method for dividing polynomials according to Euclidean geometry. This theorem states that when a polynomial P(x) is divided by a factor (x - a), which isn't really an element of the polynomial, a smaller polynomial is produced along with a remainder.
Here,
p(x) = x² + 2x + 1
g(x) = x + 1
Now,
x + 1 = 0
x = -1
Then,
p(-1) = -1² + 2 x -1 + 1 = 1 - 2 + 1 = - 1 + 1 = 0
That is,
The remainder when x² + 2x + 1 is divided by x + 1 is 0.
Learn more about remainder theorem here;
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