FACTORIZACIÓN POR FACTOR COMÚN Super facil - Para principiantes

Summary

In this video, Daniel Carreón introduces the concept of factoring by common factors, explaining it step-by-step with various examples. He covers how to identify common factors in mathematical expressions and demonstrates how to break down expressions into multiplication forms. The video includes three exercises, showing how to factor expressions like 4a + 5ab, 5x² + 7x³ - 3x, and 10a + 6a². Daniel provides detailed explanations for each step, verifying the correctness of the factorizations. The tutorial is designed to help viewers understand and apply factoring techniques in a clear and engaging way.

Takeaways

• 😀 Factorization is the process of breaking down a mathematical expression into a multiplication form.
• 😀 In factoring by common factor, you look for terms that share a common factor and then express the original equation as a multiplication.
• 😀 For the expression 4a + 5ab, the common factor is 'a', so it can be factored as a(4 + 5b).
• 😀 To verify the correctness of your factorization, multiply the common factor by the terms inside the parentheses and check if you get the original expression.
• 😀 Another example is factoring 5x² + 7x³ - 3x, where the common factor is 'x', and the factored form is x(5x + 7x² - 3).
• 😀 When multiplying, always place the number first and then the literal (variable), such as 5x² or 7x³.
• 😀 For the expression 10a + 6a², the common factor is '2a', so the factored form is 2a(5 + 3a).
• 😀 The process of factoring involves dividing each term by the common factor and simplifying the expression.
• 😀 Once you've factored the expression, verify the result by distributing the common factor back to each term inside the parentheses.
• 😀 The video encourages practicing factoring and offers additional exercises to help viewers master the concept.

Q & A

What is factorization by common factor?

Factorization by common factor is the process of breaking down a mathematical expression into a multiplication form by identifying and factoring out the common elements present in each term of the expression.

What does the process of factorization aim to achieve?

The goal of factorization is to simplify an expression and represent it as a product of simpler factors, which can make it easier to solve or analyze.

How do we identify the common factor in an expression?

To identify the common factor, we look at the terms of the expression and find the elements (such as numbers or variables) that appear in every term.

In the example 4a + 5ab, what is the common factor?

The common factor in the expression 4a + 5ab is 'a', since both terms contain the variable 'a'.

What is the factored form of 4a + 5ab?

The factored form of 4a + 5ab is 'a(4 + 5b)', where 'a' is the common factor extracted from both terms.

How can we verify if a factorization is correct?

To verify a factorization, we multiply the factored expression back out. If we return to the original expression, the factorization is correct.

In the example 5x² + 7x³ - 3x, what is the common factor?

The common factor in 5x² + 7x³ - 3x is 'x', as all the terms include the variable 'x'.

What is the factored form of 5x² + 7x³ - 3x?

The factored form of 5x² + 7x³ - 3x is 'x(5x + 7x² - 3)', with 'x' as the common factor extracted from each term.

Why is it important to factor out the greatest common factor (GCF)?

Factoring out the GCF simplifies the expression and makes it easier to manipulate or solve. It reduces the expression to its simplest form.

What is the factored form of 10a + 6a²?

The factored form of 10a + 6a² is '2a(5 + 3a)', where '2a' is the common factor extracted from both terms.

What should you do if you can't immediately spot a common factor?

If a common factor isn't immediately apparent, try looking for a number or variable that appears in all terms, or simplify the terms further (e.g., factor out any constants like 2 or 3) before proceeding.