Common Monomial Factoring - Polynomial Factoring - Grade 8 Math

Summary

In this educational video, Teacher Going explains the concept of common monomial factoring, a crucial topic in Philippine mathematics. The video guides viewers through identifying the greatest common factor (GCF) for coefficients and variables with the least exponent. It demonstrates factoring techniques using four examples, showing how to divide each term by the GCF and simplify expressions. The tutorial covers various scenarios, including factoring out common binomials, and encourages viewers to verify their work using the distributive property. The video is designed to help learners master monomial factoring and improve their mathematical skills.

Takeaways

• 📘 To factor expressions, first identify the greatest common factor (GCF) of the coefficients and the least exponent for each variable.
• 🔢 For coefficients, find the GCF by comparing the numbers and selecting the largest factor that divides both.
• 🆚 When comparing variables, choose the one with the smallest exponent to determine the GCF for that variable.
• 📉 For each term in the expression, divide by the GCF to find the remaining factors.
• 🔄 After determining the GCF, set up parentheses to represent the remaining factors of the expression.
• 📚 For expressions with multiple terms, ensure the number of terms in the factor matches the original expression.
• 🔍 When factoring, check your work by multiplying the factors back together to verify the original expression is correctly reconstructed.
• 📝 In the example with 'x' and 'y' variables, the GCF was determined to be '6xy', and the remaining factors were found by division.
• 📉 For the second example, the GCF was '9', and the remaining factors were found by dividing each term by the GCF, resulting in '4' and '-7x^2y'.
• 📚 The third example demonstrated factoring with a GCF of '2x^2', leading to factors of '1', '-2x', and '9x^3'.
• 📖 The fourth example was unique, involving factoring by grouping, where a common binomial factor 'x + 3' was extracted.

Q & A

What is the main topic discussed in the video?

The main topic discussed in the video is common monomial factoring, specifically in the context of mathematics education in the Philippines.

What is the first step in the process of common monomial factoring as described in the video?

The first step in common monomial factoring is to identify the greatest common factor (GCF) between the coefficients and the variables in the given expression.

How does the video determine the GCF for the coefficients 6 and 24?

The GCF for the coefficients 6 and 24 is determined to be 6, as it is the largest number that divides both coefficients without leaving a remainder.

What is the GCF of the variables x and x squared in the first example?

The GCF of the variables x and x squared is x, as x is the variable with the least exponent.

What is the process for finding the other factor after identifying the GCF in the video?

After identifying the GCF, the process involves dividing each term of the expression by the GCF to find the other factor, which is then placed inside a parenthesis.

How does the video handle the division of terms by the GCF for the first example?

For the first example, the terms 6xy cubed and 24x squared y are divided by the GCF 6xy, resulting in y squared and 4x as the other factors, respectively.

What is the GCF for the numbers 36 and -63 in the second example?

The GCF for the numbers 36 and -63 is 9, as it is the largest number that divides both numbers without leaving a remainder.

How does the video approach factoring when there are multiple terms with different exponents of the same variable?

The video approaches factoring by choosing the variable with the least exponent as the GCF for that variable and then dividing each term by the GCF to find the other factors.

What is the significance of the safety property of multiplication mentioned in the video?

The safety property of multiplication is mentioned as a method to check the correctness of the factoring process by multiplying the factors back to see if they yield the original expression.

How does the video handle expressions with a common binomial factor, as seen in the fourth example?

In expressions with a common binomial factor, the video suggests factoring out the common binomial first and then dividing the remaining terms by this factor to find the other factors.