--- title: Polynomial Division - Explaning Basics and Long Division description: "Polynomial division: divide one polynomial by another and read the quotient and remainder." url: https://astra-ai.co/videos/polynomials/operations-in-the-set-of-polynomials/polynomial-division/ locale: en type: video-lesson keywords: - polynomial division - dividing polynomials - quotient and remainder - long division published: 2026-10-01T09:58:05.263Z updated: 2026-10-04T22:00:30.169Z alternates: pl: https://astra-ai.co/pl/videos/wielomiany/dzialania-w-zbiorze-wielomianow/dzielenie-wielomianow/ th: https://astra-ai.co/th/videos/phahunam/bot-39-damnoenkan-phahunam/botrian-014/ sl: https://astra-ai.co/sl/videos/polinomi/operacije-s-polinomi/deljenje-polinomov/ hr: https://astra-ai.co/hr/videos/polinomi/operacije-s-polinomima/dijeljenje-polinoma/ pt: https://astra-ai.co/pt/videos/polinomios/operacoes-com-polinomios/divisao-de-polinomios/ nl: https://astra-ai.co/nl/videos/veeltermen/bewerkingen-met-polynomen/veeltermen-verdelen/ fi: https://astra-ai.co/fi/videos/polynomit/polynomien-laskutoimitukset/polynomien-jakaminen/ da: https://astra-ai.co/da/videos/polynomier/regneoperationer-med-polynomier/polynomdivision/ el: https://astra-ai.co/el/videos/polyonima/praxeis-sto-synolo-ton-polyonymon/polynomial-division/ cs: https://astra-ai.co/cs/videos/polynomy/operace-s-polynomy/deleni-polynomu/ bg: https://astra-ai.co/bg/videos/polinomi/deystviya-s-polinomi/delenie-na-polinomi/ no: https://astra-ai.co/no/videos/polynomer/operasjoner-i-mengden-av-polynomer/polynomdivisjon/ uk: https://astra-ai.co/uk/videos/polynomials-uk/uk-chapter-39/uk-polynomial-division/ ro: https://astra-ai.co/ro/videos/polinoame/operatii-in-multimea-polinoamelor/lectie-video-767c3ff9/ ms-BN: https://astra-ai.co/ms-BN/videos/polinomial/bab-c37304ab/pelajaran-767c3ff9/ id: https://astra-ai.co/id/videos/polinom/operasi-pada-himpunan-polinom/pembagian-polinom/ sv: https://astra-ai.co/sv/videos/polynom/operationer-i-mangden-av-polynom/polynomdivision/ hu: https://astra-ai.co/hu/videos/polinomok/muveletek-a-polinomok-halmazaban/polinomok-osztasa/ vi: https://astra-ai.co/vi/videos/vi-topic-01/vi-chapter-39/vi-polynomial-division/ lv: https://astra-ai.co/lv/videos/polinomi/darbibas-ar-polinomiem/stunda-767c3ff9/ lt: https://astra-ai.co/lt/videos/polinomai/veiksmai-su-polinomais/pamoka-767c3ff9/ sk: https://astra-ai.co/sk/videos/polynomy/kapitola-033/lekcia-014/ tr: https://astra-ai.co/tr/videos/polinomlar/bolum-033/ders-014/ sr: https://astra-ai.co/sr/videos/polinomi/poglavlje-033/lekcija-014/ ms: https://astra-ai.co/ms/videos/polynomials/bab-39-matematik-asas/pelajaran-014/ lo: https://astra-ai.co/lo/videos/lo-polynomials/lo-c37304ab/767c3ff9/ my: https://astra-ai.co/my/videos/my-polynomials/my-c37304ab/767c3ff9/ km: https://astra-ai.co/km/videos/polynomials/chapter-c37304ab/lesson-767c3ff9/ zh-TW: https://astra-ai.co/zh-TW/videos/polynomials/chapter-c37304ab/lesson-767c3ff9/ es-AR: https://astra-ai.co/es-AR/videos/polinomios/capitulo-33/leccion-14/ zh-HK: https://astra-ai.co/zh-HK/videos/shuxue-kecheng-001/shuxue-zhang-039/shuxue-kecheng-014/ br: https://astra-ai.co/br/videos/polinomios/capitulo-matematica-039/video-matematica-014/ en-PH: https://astra-ai.co/en-PH/videos/polynomials/chapter-c37304ab/lesson-767c3ff9/ es-PE: https://astra-ai.co/es-PE/videos/polinomios/capitulo-video-c37304ab/leccion-de-video-767c3ff9/ en-IN: https://astra-ai.co/en-IN/videos/polynomials/chapter-c37304ab/polynomial-division/ pt-TL: https://astra-ai.co/pt-TL/videos/polinomios/capitulo-de-video-033/licao-de-video-014/ mx: https://astra-ai.co/mx/videos/polinomios/capitulo-33/leccion-14/ et: https://astra-ai.co/et/videos/polunoomid/tehted-polunoomidega/polunoomide-jagamine/ es-CL: https://astra-ai.co/es-CL/videos/polinomios/capitulo-33/division-de-polinomios/ ko: https://astra-ai.co/ko/videos/polynomials-ko/33/014/ ja: https://astra-ai.co/ja/videos/polynomials-ja/33/014/ en: https://astra-ai.co/videos/polynomials/operations-in-the-set-of-polynomials/polynomial-division/ de: https://astra-ai.co/de/videos/polynome/operationen-in-der-menge-der-polynome/division-von-polynomen/ es: https://astra-ai.co/es/videos/polinomios/operaciones-con-polinomios/6-minutos/ fr: https://astra-ai.co/fr/videos/polynomes/operations-dans-lensemble-des-polynomes/division-de-polynomes/ it: https://astra-ai.co/it/videos/polinomi/operazioni-insieme-polinomi/divisione-polinomi/ --- # Polynomial Division > Polynomial division divides one polynomial by another. This lesson shows the quotient and the remainder. ## Basics of Polynomial Division Polynomial division is a process where we have two polynomials: the dividend (the polynomial we are dividing) and the divisor (the polynomial we divide by). The result is the quotient, which is also a polynomial, and in some cases we also get a remainder. ## The Division Procedure - Arrange the polynomials First, we write both polynomials in descending powers of the variable. - Divide the leading terms We divide the leading term of the dividend by the leading term of the divisor. The result becomes the next term of the quotient. - Multiply and subtract We multiply the divisor by this term of the quotient and subtract that product from the current dividend. What is left becomes the new dividend. - Repeat the process We repeat the same steps with the new dividend. We continue until the degree of the new dividend is lower than the degree of the divisor. - Remainder If the degree of the current dividend becomes smaller than the degree of the divisor and we cannot continue dividing, the remaining polynomial is the remainder.