https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-div/x2ec2f6f830c9fb89:remainder-theorem/v/polynomial-remainder-theorem 2023-10-20T17:36:47.087596279Z Intro to the Polynomial Remainder Theorem The Polynomial Remainder Theorem allows us to determine whether a linear expression is a factor of a polynomial expression easily. It tells us the remainder when a polynomial is divided by \[x - a\] is \[f(a)\]. This means if \[x - a\] is a factor of the polynomial, the remainder is zero. It's a neat trick to quickly find remainders without doing long division! video https://cdn.kastatic.org/googleusercontent/A7Mn0-RlnewSTPhArUUEQdaveGrH5a8EdaO7Ns_HHm-WbeGRBt0rbt897PMxuhOGR1V53CjTKN_FYZ8gwjaNjOtI Intro to the Polynomial Remainder Theorem The Polynomial Remainder Theorem allows us to determine whether a linear expression is a factor of a polynomial expression easily. It tells us the remainder when a polynomial is divided by \[x - a\] is \[f(a)\]. This means if \[x - a\] is a factor of the polynomial, the remainder is zero. It's a neat trick to quickly find remainders without doing long division! https://cdn.kastatic.org/ka-youtube-converted/MwG6QD352yc.mp4/MwG6QD352yc.mp4 403 Polynomial Remainder Theorem https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-div/x2ec2f6f830c9fb89:remainder-theorem/v/polynomial-remainder-theorem-example 2023-10-20T17:36:47.087596279Z Remainder theorem: finding remainder from equation The Polynomial Remainder Theorem simplifies the process of finding the remainder when dividing a polynomial by \[x - a\]. Instead of long division, you just evaluate the polynomial at \[a\]. This method saves time and space, making polynomial division more manageable. video https://cdn.kastatic.org/googleusercontent/quZZGnzpBRbxjk-FjgLDG1Kq-emvRZmMZuMsU5BFMnUCrg_ioQCgDNFHrCJF0zHoL1jCQ6n_Pd2szCh_rb0UNuA Remainder theorem: finding remainder from equation The Polynomial Remainder Theorem simplifies the process of finding the remainder when dividing a polynomial by \[x - a\]. Instead of long division, you just evaluate the polynomial at \[a\]. This method saves time and space, making polynomial division more manageable. https://cdn.kastatic.org/ka-youtube-converted/MHtTP6vc4RU.mp4/MHtTP6vc4RU.mp4 212 Polynomial Remainder Theorem https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-div/x2ec2f6f830c9fb89:remainder-theorem/v/remainder-theorem-examples 2022-10-06T23:23:50.639907812Z Remainder theorem examples The polynomial remainder theorem says that for a polynomial p(x) and a number a, the remainder on division by (x-a) is p(a). This might not be very clear right now, but you will understand this much better after watching these examples. video https://cdn.kastatic.org/googleusercontent/5aN7YgK9otiLJNXThl4FXsrevlvXF-l1GBZdTkap6i7Rnxxi3r8Riusyk5RaoKRHJKdd3xBcOowKgJDpNMXGN0At Remainder theorem examples The polynomial remainder theorem says that for a polynomial p(x) and a number a, the remainder on division by (x-a) is p(a). This might not be very clear right now, but you will understand this much better after watching these examples. https://cdn.kastatic.org/ka-youtube-converted/dBOpC_-PDTA.mp4/dBOpC_-PDTA.mp4 332 Polynomial Remainder Theorem https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-div/x2ec2f6f830c9fb89:remainder-theorem/e/remainder-theorem-of-polynomials 2026-04-30T21:00:44.23618726Z Remainder theorem Use the PRT (Polynomial Remainder Theorem) to determine the factors of polynomials and their remainders when divided by linear expressions. Tomer Gal exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-div/x2ec2f6f830c9fb89:remainder-theorem/v/polynomial-remainder-theorem-to-test-factor 2023-10-20T17:43:07.031962377Z Remainder theorem: checking factors Learn how to determine if an expression is a factor of a polynomial by dividing the polynomial by the expression. If the remainder is zero, the expression is a factor. The video also demonstrates how to quickly calculate the remainder using the theorem. video https://cdn.kastatic.org/googleusercontent/tkGhvHyKpq6K3De7Cwc80o7hzjiMECXGyKU2bo_a7LWT0WMvBVv_nEyeIkL3AjFl8tPYJKpSDOPiLPHq3BgIz8iV Remainder theorem: checking factors Learn how to determine if an expression is a factor of a polynomial by dividing the polynomial by the expression. If the remainder is zero, the expression is a factor. The video also demonstrates how to quickly calculate the remainder using the theorem. https://cdn.kastatic.org/ka-youtube-converted/JAdNNJynWM4.mp4/JAdNNJynWM4.mp4 206 Polynomial Remainder Theorem https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-div/x2ec2f6f830c9fb89:remainder-theorem/v/constructing-a-polynomial-that-has-a-certain-factor 2023-10-20T17:43:07.031962377Z Remainder theorem: finding coefficients Learn how to find the value of 'c' that makes 'x - 5' a factor of a polynomial 'p(x)'. Understand how setting 'p(5)' equal to zero and solving for 'c' unveils the mystery. Grasp the concept of the Polynomial Remainder Theorem with a real example. video https://cdn.kastatic.org/googleusercontent/Z_g8jpkRj6QxDJ5OyuxQbwiTC5VwqdgUfnidyuhBJ0BnvMDdLkcjkB2G200WNSKiJQ1ItIP6Y1UdXcSKSgYrUeyN Remainder theorem: finding coefficients Learn how to find the value of 'c' that makes 'x - 5' a factor of a polynomial 'p(x)'. Understand how setting 'p(5)' equal to zero and solving for 'c' unveils the mystery. Grasp the concept of the Polynomial Remainder Theorem with a real example. https://cdn.kastatic.org/ka-youtube-converted/e0lBUViss8E.mp4/e0lBUViss8E.mp4 219 Polynomial Remainder Theorem https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-div/x2ec2f6f830c9fb89:remainder-theorem/e/remainder-theorem-and-factors 2025-02-27T11:46:16.621461116Z Remainder theorem and factors Students analyze factors of polynomials by using the polynomial remainder theorem. Tomer Gal exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-div/x2ec2f6f830c9fb89:remainder-theorem/v/polynomial-remainder-theorem-proof 2021-06-30T17:32:37Z Proof of the Polynomial Remainder Theorem The PRT (Polynomial Remainder Theorem) may seem crazy to prove, but Sal shows how you can do it in less than six minutes! video https://cdn.kastatic.org/googleusercontent/yvREG4WnLP3xzjrWptaRocG-65mBtoZQMiDgW8Hx1L_Cyy3dEfAi1OAMDSxmS-SR59GoQrImsqiThpQYhy1JrgCT Proof of the Polynomial Remainder Theorem The PRT (Polynomial Remainder Theorem) may seem crazy to prove, but Sal shows how you can do it in less than six minutes! https://cdn.kastatic.org/ka-youtube-converted/NIazpCER9oM.mp4/NIazpCER9oM.mp4 342 Polynomial Remainder Theorem https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-div/x2ec2f6f830c9fb89:remainder-theorem/a/polynomial-division-faq 2022-11-24T02:28:55.815015347Z Polynomial division: FAQ Frequently asked questions about polynomial division article