Factoring difference of squares: shared factors | High School Math | Khan Academy

TL;DR

Learn how to factor quadratic expressions and find the common binomial factor between two given expressions.

Transcript

• [Voiceover] We're told that the quadratic expressions m squared minus 4m minus 45, and 6m squared minus 150, share a common binomial factor. What binomial factor do they share? And like always pause the video and see if you can work through this. All right, now let's work through this together and the way I am going to do this is I'm just going t... Read More

Key Insights

• ❎ Quadratic expressions with a coefficient of 1 for the squared term can be factored as (m + a)(m + b), where a + b equals the coefficient of the squared term, and a * b equals the constant term.
• 😑 Finding the common binomial factor between two expressions involves factorizing each expression separately and identifying the common term.
• 🍉 The constant term in a quadratic expression helps in determining possible pairs of numbers whose product equals the constant term, leading to the binomial factors.
• 😑 Factoring quadratic expressions is a crucial skill in mathematics as it simplifies algebraic expressions and enables equation solving and root finding.

Questions & Answers

Q: How do you factor a quadratic expression when the coefficient of the squared term is 1?

To factor a quadratic expression with a coefficient of 1 for the squared term, determine two numbers whose product is equal to the constant term and whose sum is equal to the coefficient of the squared term. These numbers will be used as constants in the binomial factors.

Q: What does it mean for two expressions to share a common binomial factor?

When two expressions share a common binomial factor, it means that both expressions can be factored into the same binomial factor and additional terms, if any. This common binomial factor can be found by factorizing each expression separately and identifying the common term.

Q: How can the constant term in a quadratic expression help in determining the binomial factors?

The constant term in a quadratic expression allows us to find possible products of two numbers that equal the constant term. Since the product is negative, the two numbers will have different signs. The pair of numbers whose product equals the constant term and whose sum equals the coefficient of the squared term gives the binomial factors.

Q: Why is factoring important in mathematics?

Factoring is important in mathematics as it allows us to simplify and solve equations, manipulate algebraic expressions, and find roots of polynomials. It helps in understanding the underlying structure of mathematical expressions and facilitates various calculations and problem-solving techniques.

Summary & Key Takeaways

• The video explains how to factor quadratic expressions and determine the common binomial factor between two given expressions.

• For a quadratic expression with a coefficient of 1 for the squared term, it can be factored as (m + a)(m + b), where a + b equals the coefficient of the squared term, and a * b equals the constant term.

• By finding two numbers whose product is equal to the constant term and whose sum is equal to the coefficient of the squared term, the quadratic expression can be factored as a product of two binomials.