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Remainder Theorem
Remainder Theorem: A polynomial f(x) when divided by (x - a) will have a remainder equal to f(a). Key Points: A polynomial f(x) divided by (x - a) res...
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Remainder Theorem: A polynomial f(x) when divided by (x - a) will have a remainder equal to f(a). Key Points: A polynomial f(x) divided by (x - a) res...
Remainder Theorem:
A polynomial f(x) when divided by (x - a) will have a remainder equal to f(a).
Key Points:
A polynomial f(x) divided by (x - a) results in a quotient f(x) + q(x), where q(x) is the remainder.
The remainder theorem allows us to evaluate f(a) by substituting a into the expression for q(x).
The remainder theorem can be applied to any polynomial, regardless of its degree or coefficients.
Examples:
If f(x) = x^2 + 3x + 2, then f(3) = 9, as (3)^2 + 3(3) + 2 = 9.
If f(x) = x^3 - 2x + 1, then f(-1) = 1, as (-1)^3 - 2(-1) + 1 = 1.
The remainder theorem is a powerful tool for finding the value of a polynomial at a given point. It is used extensively in mathematics, particularly in areas such as polynomial manipulation, factoring, and finding critical points of polynomials