Grade 8 MATH Term 1 Week 3, 4, 5: Factoring Common Monomial Factor | MATATAG - Quarter 1 (Tagalog)

The video introduces the topic of factoring polynomials, specifically focusing on factoring out a common monomial factor. It outlines the learning competency, which is to factor different types of polynomials, and previews future topics like the difference of two squares, quadratic trinomials, and perfect square trinomials.

A real-life problem about expanding a garden is used to review the multiplication of binomials and monomials. The gardener, Aya, expands her garden, creating a rectangular bed with a width of 'x' and a length of 'x + 2'. The area is calculated as x * (x + 2), which, using the distributive property, results in x² + 2x.

The video poses a follow-up question: how to find the original dimensions (length and width) from the area expression (x² + 2x)? This introduces the concept of factoring as the reverse process of multiplication, breaking down expressions to find their components. It confirms that factoring out the common monomial factor is the first technique to be discussed.

Using the garden example (x² + 2x), the video demonstrates the steps for factoring out a common monomial factor: (1) Break down each term into prime factors (x*x for x² and 2*x for 2x). (2) Identify and factor out the greatest common factor (GCF). In this case, 'x' is the GCF. The factored form is x(x + 2).

Two more examples are provided to solidify the concept. The first example is factoring 6x² - 9x, where the GCF is found to be 3x, resulting in the factored form 3x(2x - 3). The second example is factoring 5x²y + 15xy, with a GCF of 5xy, yielding 5xy(x + 3).

A more complex example, 12a³b²c - 18a²b³c, is presented. The GCF is identified as 6a²b²c, leading to the factored form 6a²b²c(2a - 3b). The video also mentions that with practice, students can find factors without explicitly listing all prime factors.

The video offers practice exercises for viewers to solve, then reveals the correct answers to check understanding. It encourages viewers to verify their answers by multiplying the factors using the distributive property. The video concludes by previewing the next lesson: factoring the difference of two squares.