FACTORIZAR TRINOMIOS ax^2+.bx+c: La factorización con la que no pueden los estudiantes

Factoring a trinomial of the form ax² + bx + c when the leading coefficient a is not 1 can seem like a real nightmare. In this video, you'll learn how to factor the trinomial 8x² + 2x − 3 step by step, understanding the reason behind each transformation and without resorting to a rote memorization of rules. Factoring involves writing an expression as a product of simpler factors. Just as we can write 15 = 3 × 5, our goal is to transform the trinomial 8x² + 2x − 3 into a product of two binomials. To achieve this, we'll use two fundamental notable identities: (a + b)² = a² + 2ab + b² a² − b² = (a + b)(a − b) The first step is to conveniently introduce a factor of 8 so that the quadratic term inside the parentheses is x². Next, we complete the square by adding and subtracting the same amount to avoid changing the expression's value. This transforms the trinomial into a difference of squares: 8[(x + 1/8)² − (5/8)²] Then, we apply the difference of squares identity and carefully simplify the factors until we arrive at the final factorization: 8x² + 2x − 3 = (4x + 3)(2x − 1) At the end of this explanation, you'll find an exercise for you to practice on your own: factor 6m² − 7m − 3. In this case, you'll need to complete the square using the identity (a − b)² = a² − 2ab + b² and then apply the difference of squares identity again. CHAPTERS 0:00 The Problem of Factoring Trinomials 0:14 Trinomials of the Form ax² + bx + c 0:39 Example: 8x² + 2x − 3 0:45 What It Means to Factor a Polynomial 1:13 The Two Notable Identities We Will Use 1:59 Strategy for Completing the Square 2:27 How to Make the Coefficient of x² 1 3:27 Introducing the Factor 8 4:42 Adding a Zero Conveniently 5:02 Identifying the Structure of the Perfect Square 6:04 Adding and Subtracting (1/8)² 7:12 Finding the Square of a Binomial 7:49 Simplifying Fractions 8:46 Transforming into a Difference of Squares 9:34 Applying a² − b² = (a + b)(a − b) 10:44 Simplifying the two factors 11:40 Dividing the factor 8 12:18 Final factorization 12:54 Why understanding the procedure is important 13:01 Proposed exercise: 6m² − 7m − 3 More polynomial factorization exercises here:    • Factorizar polinomios   #Factoring #mathwithjuan #Algebra You'd help me a lot if you became a member of MATH WITH JUAN    / @matematicaconjuan