remainder theorem

2024-05-14


Learn how to use the polynomial remainder theorem to find the value of a polynomial function at a given point. Watch examples, see graphs, and read comments from other learners.

Solution: By the remainder theorem formula, the remainder when p (x) is divided by (ax + b) is p (-b/a). Thus: a) x - 2 = 0 ⇒ x = 2. Thus, the remainder when f (x) is divided by (x - 2) is f (2). b) 2x - 1 = 0 ⇒ x = 1/2. Thus, the remainder when g (x) is divided by (2x - 1) is g (1/2). c) 3x + 4 = 0 ⇒ x = -4/3.

Learn how to divide one polynomial by another using the Remainder Theorem, a rule that provides certain conditions for the quotient and the remainder. See examples of dividing polynomials by monomials, non-zero polynomials and other polynomials, and how to use the remainder as a zero of the dividend.

Learn how to use the remainder theorem to find the remainder of a polynomial division by a linear polynomial. See the statement, proof, examples, and differences with the factor theorem.

Learn how to use the Remainder Theorem to calculate the remainder of a polynomial divided by some linear factor in a simple and direct way. See examples of using the theorem with long division and synthetic division methods, and verify your answers with the Remainder Theorem.

Remainder Theorem. The Remainder Theorem states that if a polynomial f (x) of degree n (≥ 1) is divided by a linear polynomial (a polynomial of degree 1) g (x) of the form (x - a), the remainder of this division is the same as the value obtained by substituting r (x) = f (a) into the polynomial f (x). Mathematically,

Learn how to use the remainder theorem of polynomials to find the remainder of any division of a polynomial by a linear polynomial. See the statement, proof, and examples of the theorem with step-by-step solutions. Compare with factor theorem and practice with practice problems.

Learn how to use the Polynomial Remainder Theorem to determine whether a linear expression is a factor of a polynomial expression. Watch a video, see examples, and practice with questions and comments.

Learn how to use the remainder theorem to find the remainder of a polynomial division without doing the whole division. See the definition, proof and examples of the theorem and its special case, the factor theorem.

Learn how to use the polynomial remainder theorem to simplify dividing a polynomial by x - a. See an example of finding the remainder by evaluating the polynomial at a.

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