https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-zeros/v/polynomial-zeros-introduction 2022-10-06T23:23:50.639907812Z Zeros of polynomials introduction The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero. They are interesting to us for many reasons, one of which is that they tell us about the x-intercepts of the polynomial's graph. We will also see that they are directly related to the factors of the polynomial. video https://cdn.kastatic.org/googleusercontent/AI72TlzUEF41olEgrUdZCNH1O1KIT85sX3KZdY7j4dNue4fjseG_zfULUUFRKVY1cXrQtv3iBCZ_TrTP9epsLTPD Zeros of polynomials introduction The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero. They are interesting to us for many reasons, one of which is that they tell us about the x-intercepts of the polynomial's graph. We will also see that they are directly related to the factors of the polynomial. https://cdn.kastatic.org/ka-youtube-converted/EtzwLlkoAnM.mp4/EtzwLlkoAnM.mp4 309 Zeros of polynomials https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-zeros/v/plot-polynomial-zeros 2022-10-06T23:23:50.639907812Z Zeros of polynomials: plotting zeros When we are given a polynomial in factored form, we can quickly find the polynomial's zeros. Then, we can represent them as the x-intercepts of the polynomial's graph. video https://cdn.kastatic.org/googleusercontent/T3nrVwwXlgKU6JKXXyehZIjMg-nzxgIbIo2uoZ7pEnULeENw1ppE4w5p4gXwoWX5bLG3v3gxsraYr5w40c55qkbv7A Zeros of polynomials: plotting zeros When we are given a polynomial in factored form, we can quickly find the polynomial's zeros. Then, we can represent them as the x-intercepts of the polynomial's graph. https://cdn.kastatic.org/ka-youtube-converted/5qQUN1fugXQ.mp4/5qQUN1fugXQ.mp4 199 Zeros of polynomials https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-zeros/v/polynomial-equation-from-zeros 2022-10-06T23:23:50.639907812Z Zeros of polynomials: matching equation to zeros When we are given a list of the zeros of a polynomial, we can conclude the polynomial must have certain factors, which gives us information about the equation of the polynomial. video https://cdn.kastatic.org/googleusercontent/Gu1jgT9diQBt_0C4Uq1vFqy8vfFYG_AbpL0aSDCXTPk1uU86yb6rj1b6K0oPmvA3uO0yLtDxRbFDbURg4hCjpbOMsQ Zeros of polynomials: matching equation to zeros When we are given a list of the zeros of a polynomial, we can conclude the polynomial must have certain factors, which gives us information about the equation of the polynomial. https://cdn.kastatic.org/ka-youtube-converted/CtqwiX4wHEY.mp4/CtqwiX4wHEY.mp4 231 Zeros of polynomials https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-zeros/v/polynomial-equation-from-graph 2022-10-06T23:23:50.639907812Z Zeros of polynomials: matching equation to graph When we are given the graph of a polynomial, we can deduce what its zeros are, which helps us determine a few factors the polynomial's equation must include. video https://cdn.kastatic.org/googleusercontent/_9vCMWZbEEY1_vyVV7b1RuIobA9TxlR-Z20ef1APoLRx1QwcfgQPW4pLl15gJpluAETwzCUnt9RMTkfHh5gmnjE Zeros of polynomials: matching equation to graph When we are given the graph of a polynomial, we can deduce what its zeros are, which helps us determine a few factors the polynomial's equation must include. https://cdn.kastatic.org/ka-youtube-converted/f-xluUaAfwo.mp4/f-xluUaAfwo.mp4 181 Zeros of polynomials https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-zeros/e/using-zeros-to-graph-polynomials 2026-04-08T01:15:04.085520103Z Zeros of polynomials (factored form) Select the graph that best suits a polynomial equation by considering the zeros of the polynomial. Tomer Gal exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-zeros/v/polynomial-zeros-grouping 2022-10-06T23:23:50.639907812Z Zeros of polynomials (with factoring): grouping When a polynomial is given in factored form, we can quickly find its zeros. When its given in expanded form, we can factor it, and then find the zeros! Here is an example of a 3rd degree polynomial we can factor using the method of grouping. video https://cdn.kastatic.org/googleusercontent/iqDTC9bfViwTQSrnQICYjOCOzFgEG7UGBBczp2Aq4gwjrgXogT2eEOhUZSsPltn9nqdeBgSr-JG0EKJa7T62BN2l Zeros of polynomials (with factoring): grouping When a polynomial is given in factored form, we can quickly find its zeros. When its given in expanded form, we can factor it, and then find the zeros! Here is an example of a 3rd degree polynomial we can factor using the method of grouping. https://cdn.kastatic.org/ka-youtube-converted/w0vTAHIS5B4.mp4/w0vTAHIS5B4.mp4 295 Zeros of polynomials https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-zeros/v/polynomial-zeros-common-factor 2022-10-06T23:23:50.639907812Z Zeros of polynomials (with factoring): common factor When a polynomial is given in factored form, we can quickly find its zeros. When it's given in expanded form, we can factor it, and then find the zeros! Here is an example of a 3rd degree polynomial we can factor by first taking a common factor and then using the sum-product pattern. video https://cdn.kastatic.org/googleusercontent/0zIjZ0ASt2tv6tFK-GrZbcOHjU4J07rt0uQ8QU6LVoH3cPbE11TXWCsAwtxXRVdvnaVBfaBNtpZtx1cG4e35pOI Zeros of polynomials (with factoring): common factor When a polynomial is given in factored form, we can quickly find its zeros. When it's given in expanded form, we can factor it, and then find the zeros! Here is an example of a 3rd degree polynomial we can factor by first taking a common factor and then using the sum-product pattern. https://cdn.kastatic.org/ka-youtube-converted/SONskIMkYdU.mp4/SONskIMkYdU.mp4 212 Zeros of polynomials https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-zeros/e/find-the-zeros-of-polynomials 2026-04-07T23:17:37.123726494Z Zeros of polynomials (with factoring) Use various methods in order to find all the zeros of polynomial expressions or functions. Tomer Gal exercise