https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-intro/v/factor-completely-common-factor 2022-09-10T01:04:29.754011735Z Factoring completely with a common factor We can factor quadratics by first pulling out a common factor so the result looks like a(x+b)(x+c). Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/e369c3aa-6d22-4301-a1d5-01e216df7153_1280_720_base.png Factoring completely with a common factor We can factor quadratics by first pulling out a common factor so the result looks like a(x+b)(x+c). https://cdn.kastatic.org/ka-youtube-converted/FoTD41xzF5Q.mp4/FoTD41xzF5Q.mp4 240 Factoring polynomials https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-intro/v/factoring-quadratics-common-factor 2022-09-10T01:04:29.754011735Z Factoring quadratics with a common factor We can factor quadratics by first pulling out a common factor so the result looks like a(x+b)(x+c). Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/c80e1ddd-8b4a-4848-9e5a-283c4549e8a3_1280_720_base.png Factoring quadratics with a common factor We can factor quadratics by first pulling out a common factor so the result looks like a(x+b)(x+c). https://cdn.kastatic.org/ka-youtube-converted/m6uOqU91ypI.mp4/m6uOqU91ypI.mp4 185 Factoring polynomials https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-intro/e/factor-quadratics-common-factor 2023-12-12T00:32:03.629852833Z Factoring quadratics with a common factor Practice factoring quadratics by first pulling out a common factor so the result looks like a(x+b)(x+c). Jeff Dodds exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-difference-squares/v/difference-of-squares-intro 2022-10-06T23:01:00.745424633Z Difference of squares intro When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5). This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b). video https://cdn.kastatic.org/ka_thumbnails_cache/c52b1b59-e0b8-4b92-931b-13024c98d84f_1280_720_base.png Difference of squares intro When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5). This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b). https://cdn.kastatic.org/ka-youtube-converted/HLNSouzygw0.mp4/HLNSouzygw0.mp4 294 Factoring polynomials https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-difference-squares/e/factoring_difference_of_squares_1 2025-01-15T08:58:52.349960688Z Difference of squares intro Factor quadratic expressions into the special products of the general form (x+a)(x-a). Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-difference-squares/e/factoring_difference_of_squares_2 2025-02-13T04:57:25.728250847Z Difference of squares Factor quadratic expressions of the general difference of squares form: (ax)^2-b^2. The factored expressions have the general form (ax+b)(ax-b). Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-difference-squares/a/factoring-quadratics-difference-of-squares 2021-06-30T17:32:36Z Factoring quadratics: Difference of squares Learn how to factor quadratics that have the "difference of squares" form. For example, write x²-16 as (x+4)(x-4). article https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/v/identifying-perfect-square-trinomials 2022-10-06T23:01:00.745424633Z Identifying perfect square form Sal shows how we can identify that a trinomial has the "perfect square" form. video https://cdn.kastatic.org/ka_thumbnails_cache/047b2592-ee51-42a7-99ce-80bf83c0ec6d_1280_720_base.png Identifying perfect square form Sal shows how we can identify that a trinomial has the "perfect square" form. https://cdn.kastatic.org/ka-youtube-converted/4STGvuoBi5U.mp4/4STGvuoBi5U.mp4 277 Factoring polynomials https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/v/perfect-square-factorization-intro 2022-10-06T23:01:00.745424633Z Perfect square factorization intro When an expression has the general form a²+2ab+b², then we can factor it as (a+b)². For example, x²+10x+25 can be factored as (x+5)². This method is based on the pattern (a+b)²=a²+2ab+b², which can be verified by expanding the parentheses in (a+b)(a+b). video https://cdn.kastatic.org/ka_thumbnails_cache/65b779ae-9d58-4d2d-ab39-c5bde1a9f75b_1280_720_base.png Perfect square factorization intro When an expression has the general form a²+2ab+b², then we can factor it as (a+b)². For example, x²+10x+25 can be factored as (x+5)². This method is based on the pattern (a+b)²=a²+2ab+b², which can be verified by expanding the parentheses in (a+b)(a+b). https://cdn.kastatic.org/ka-youtube-converted/JX5Zvh6swmo.mp4/JX5Zvh6swmo.mp4 319 Factoring polynomials https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/v/factoring-perfect-square-trinomials 2021-06-30T17:32:36Z Factoring perfect squares Sal factors 25x^2-30x+9 as (5x-3)^2 or as (-5x+3)^2. Sal Khan video https://cdn.kastatic.org/googleusercontent/5CcqYMA3KWSrPBPUIZtt517ekwwGim7xFbY5srOQz-sjX2oU8wcAZl9sfpgf1c2n-lp9F0kfBDeiDkPx4lPUTg Factoring perfect squares Sal factors 25x^2-30x+9 as (5x-3)^2 or as (-5x+3)^2. https://cdn.kastatic.org/ka-youtube-converted/liRNTieIU_k.mp4/liRNTieIU_k.mp4 294 Factoring polynomials https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/v/u09-l2-t1-we1-factoring-special-products-1 2021-06-30T17:32:40Z Factoring perfect squares: negative common factor Sal factors -4t^2-12t-9 as -1(2t+3)^2. Sal Khan video https://cdn.kastatic.org/googleusercontent/Nl1cABXDYkAXNM_cQMBiqnF9iPmHCtgDQ1loFqq5nsVwq-ck4N9Makwff1aq68C_Sxjo3OUXuDr04EmOdsH_AgMh Factoring perfect squares: negative common factor Sal factors -4t^2-12t-9 as -1(2t+3)^2. https://cdn.kastatic.org/ka-youtube-converted/XuwldEyWjH0.mp4/XuwldEyWjH0.mp4 232 Factoring polynomials https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/e/intro-to-factoring-perfect-squares 2025-01-15T08:58:52.349960688Z Perfect squares intro Factor quadratic expressions into the special products of the general form (x+a)² or (x-a)². Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/e/factoring-perfect-squares 2025-02-18T07:52:09.551150445Z Perfect squares Factor quadratic expressions of the general perfect square forms: (ax)²+2abx+b² or (ax)²-2abx+b². The factored expressions have the general forms (ax+b)² or (ax-b)². Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/a/factoring-quadratics-perfect-squares 2023-07-28T22:30:23.739634445Z Factoring quadratics: Perfect squares Learn how to factor quadratics that have the "perfect square" form. For example, write x²+6x+9 as (x+3)². article https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-intro/v/factoring-simple-quadratic-expression 2022-10-06T23:01:00.745424633Z Factoring quadratics as (x+a)(x+b) Sal factors x²-3x-10 as (x+2)(x-5) using the sum-product form: (x+a)(x+b)=x²+(a+b)x+a*b. video https://cdn.kastatic.org/ka_thumbnails_cache/4673d59c-5e5f-4b46-acfb-9b882ee3f074_1280_720_base.png Factoring quadratics as (x+a)(x+b) Sal factors x²-3x-10 as (x+2)(x-5) using the sum-product form: (x+a)(x+b)=x²+(a+b)x+a*b. https://cdn.kastatic.org/ka-youtube-converted/D3a8NnpQ2vU.mp4/D3a8NnpQ2vU.mp4 394 Factoring polynomials https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-intro/v/factoring-polynomials-1 2021-06-30T17:32:38Z Factoring quadratics as (x+a)(x+b) (example 2) Sal factors x^2-14x+40 as (x-4)(x-10) and x^2-x-12 as (x+3)(x-4). Sal Khan video https://cdn.kastatic.org/googleusercontent/hDf2C8KEnro0EoyPkY-KoGVoUhyBF99uFQQ9YtHKysIYhi-7-wNY91zjnOeRnx0qlxQiAw1UWg9tSkuOWYhXtZI Factoring quadratics as (x+a)(x+b) (example 2) Sal factors x^2-14x+40 as (x-4)(x-10) and x^2-x-12 as (x+3)(x-4). https://cdn.kastatic.org/ka-youtube-converted/1kfq0aR3ASs.mp4/1kfq0aR3ASs.mp4 260 Factoring polynomials https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-intro/v/factoring-quadratic-expressions 2021-06-30T17:32:40Z More examples of factoring quadratics as (x+a)(x+b) Can't get enough of Sal factoring simple quadratics? Here's a handful of examples just for you! Sal Khan video https://cdn.kastatic.org/googleusercontent/jes3qWMgnpoQTzMnk6gBG4LPGvEkBuNZ_51RvA8AztJSOEIHpzxj3ldk8K6VXFIwjoNETD8E7TCU_iXiI2VrdUg More examples of factoring quadratics as (x+a)(x+b) Can't get enough of Sal factoring simple quadratics? Here's a handful of examples just for you! https://cdn.kastatic.org/ka-youtube-converted/eF6zYNzlZKQ.mp4/eF6zYNzlZKQ.mp4 990 Factoring polynomials https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/v/solving-for-constants-in-perfect-square-polynomial 2022-10-06T23:01:00.745424633Z Factoring perfect squares: missing values Sal analyzes the factorization of x^2+5x+c as (x+d)^2 to find the values of the missing coefficients c and d. video https://cdn.kastatic.org/ka_thumbnails_cache/05e7285c-91e3-4696-aa50-3f68d61ae805_1280_720_base.png Factoring perfect squares: missing values Sal analyzes the factorization of x^2+5x+c as (x+d)^2 to find the values of the missing coefficients c and d. https://cdn.kastatic.org/ka-youtube-converted/oIslHyWJHEY.mp4/oIslHyWJHEY.mp4 159 Factoring polynomials https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-intro/e/factoring_polynomials_1 2025-02-18T07:52:09.551150445Z Factoring quadratics intro Factor quadratics of the form x²+bx+c. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-intro/a/factoring-quadratics-leading-coefficient-1 2022-09-10T01:04:29.754011735Z Factoring quadratics: leading coefficient = 1 Learn how to factor quadratic expressions as the product of two linear binomials. For example, x²+5x+6=(x+2)(x+3). article https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-intro/a/factoring-simple-quadratics-review 2021-06-30T17:32:39Z Factoring simple quadratics review Factoring quadratics is very similar to multiplying binomials, just going the other way. For example, x^2+3x+2 factors to (x+1)(x+2) because (x+1)(x+2) multiplies to x^2+3x+2. This article reviews the basics of how to factor quadratics into the product of two binomials. article