https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-intervals/v/polynomial-zero-multiplicity 2022-10-06T23:23:50.639907812Z Multiplicity of zeros of polynomials The polynomial p(x)=(x-1)(x-3)² is a 3rd degree polynomial, but it has only 2 distinct zeros. This is because the zero x=3, which is related to the factor (x-3)², repeats twice. This is called multiplicity. It means that x=3 is a zero of multiplicity 2, and x=1 is a zero of multiplicity 1. Multiplicity is a fascinating concept, and it is directly related to graphical behavior of the polynomial around the zero. video https://cdn.kastatic.org/googleusercontent/JtVOYUJ3kbXUviC7hIWdbTWEutr7ii6lU_8VGVk2LAyPM0kYT5sO8vsBMWCWXjpazxwoOk7-6zt1mf4-vyL4ZTh4 Multiplicity of zeros of polynomials The polynomial p(x)=(x-1)(x-3)² is a 3rd degree polynomial, but it has only 2 distinct zeros. This is because the zero x=3, which is related to the factor (x-3)², repeats twice. This is called multiplicity. It means that x=3 is a zero of multiplicity 2, and x=1 is a zero of multiplicity 1. Multiplicity is a fascinating concept, and it is directly related to graphical behavior of the polynomial around the zero. https://cdn.kastatic.org/ka-youtube-converted/jrFLb9ZoZH0.mp4/jrFLb9ZoZH0.mp4 396 Multiplicity of zeros of polynomials https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-intervals/v/polynomial-multiplicity-examples 2022-10-06T23:23:50.639907812Z Zeros of polynomials (multiplicity) Given the graph of a polynomial and looking at its x-intercepts, we can determine the factors the polynomial must have. Additionally, we can determine whether those factors are raised to an odd power or to an even power (this is called the multiplicity of the factors). video https://cdn.kastatic.org/ka_thumbnails_cache/8128dbd2-af16-4742-a825-2f2c559e2496_1280_720_base.png Zeros of polynomials (multiplicity) Given the graph of a polynomial and looking at its x-intercepts, we can determine the factors the polynomial must have. Additionally, we can determine whether those factors are raised to an odd power or to an even power (this is called the multiplicity of the factors). https://cdn.kastatic.org/ka-youtube-converted/1ke_xceCevk.mp4/1ke_xceCevk.mp4 300 Multiplicity of zeros of polynomials https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-intervals/e/poly-zeros-mult 2026-04-30T21:00:44.23618726Z Zeros of polynomials (multiplicity) Relate polynomials to their graphs, where the polynomials have zeros with multiplicity greater than 1. Tomer Gal exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-intervals/a/zeros-of-polynomials-and-their-graphs 2023-02-11T00:49:50.919025829Z Zeros of polynomials & their graphs Learn about the relationship between the zeros, roots, and x-intercepts of polynomials. Learn about zeros multiplicities. article