Factoring quadratics as (x+a)(x+b) (example 2) | Mathematics II | High School Math | Khan Academy | Summary and Q&A

TL;DR

Learn how to factor second degree expressions by finding two numbers that add up to the coefficient on the x term and multiply to equal the constant term.

Key Insights

• 😑 Factoring a second degree expression involves finding two numbers that add up to the coefficient on the x term and multiply to equal the constant term.
• 🤘 The sign of the coefficient and constant determines the sign of the two numbers in the factored expression.
• #️⃣ Trial and error is often necessary to find the correct numbers for factoring.

Transcript

To better understand how we can factor second degree expressions like this, I'm going to go through some examples. We'll factor this expression and we'll factor this expression. And hopefully it'll give you a background on how you could generally factor expressions like this. And to think about it, let's think about what happens if I were to multip... Read More

Questions & Answers

Q: How do you factor a second degree expression?

To factor a second degree expression, you need to find two numbers that add up to the coefficient on the x term and multiply to equal the constant term.

Q: What happens if the coefficient and constant in the expression are both positive?

If the coefficient and constant are both positive, the two numbers in the factored expression will both be negative.

Q: How do you determine if the two numbers in the factored expression should be positive or negative?

The sign of the coefficient and constant term determines the sign of the two numbers in the factored expression. If they are both positive or both negative, the two numbers will be negative.

Q: Is there a systematic method for factoring second degree expressions?

Factoring second degree expressions often involves trial and error, trying different combinations of numbers until you find two that satisfy the conditions of adding up to the coefficient and multiplying to the constant term.

Summary & Key Takeaways

• Factoring involves finding two numbers that, when added, equal the coefficient on the x term and, when multiplied, equal the constant term.

• If the coefficient and constant are both positive or both negative, the two numbers in the factored expression will both be negative.

• Trial and error is often necessary to find the correct numbers for factoring.