The remainder when x³- 3x² + 5x - 7 is divided by x - 2 is -1.
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 - 2x^2 + 5x - 7[/tex]
We have to find the remainder of polynomial f(x) when divided by (x - 2).
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(2).
Plug x = 2 is given polynomial f(x).
[tex]f(2) = (2)^3 - 3(2)^2 + 5(2) - 7 \\f(2) = 8 - 12 + 10 - 7\\f(2) = -1[/tex]
Hence, the remainder when x³- 3x² + 5x - 7 is divided by x - 2 is -1.
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Complete question:
When x³- 3x²+ 5x - 7 is divided by x - 2 then the remainder is?
