Example 7: Factor a polynomial with two variables by grouping | Algebra I | Khan Academy

TL;DR

Learn how to factor expressions by grouping when there is no common factor across all terms.

Transcript

We're asked to factor this expression by grouping. Now, they mention grouping, we're going to see what grouping is, but we're going to see very quickly that we have to do this thing called grouping because you can't just factor this expression. If you look at these, each of the terms, all but one of them is divisible by 5. So you can't just factor ... Read More

Key Insights

• 😑 Grouping is necessary when there is no common factor across all terms in an expression.
• 😑 Look for terms with common factors to simplify the expression.
• 😑 The factored expression can be verified by distributing each expression obtained after factoring.

Questions & Answers

Q: Why is grouping necessary to factor expressions?

Grouping is necessary because not all terms in the expression have a common factor. By grouping terms with common factors together, we can simplify the expression and make it easier to factor.

Q: How do we identify which terms to group together?

Look for terms that share common factors. In the provided example, the terms 5rs and 25r have the common factors 5 and r, so they are grouped together. Similarly, the terms -3s and 15 have the common factor -3, so they are grouped together.

Q: Can we verify if the factoring is done correctly?

Yes, we can verify the factoring by distributing each expression obtained after factoring back into the original expression. If the expanded expressions match the original expression, then the factoring is correct.

Q: Is it possible to further simplify the factored expression?

Yes, it is possible. After factoring the two groups, we may notice that they have a common factor, as seen in the example with (s + 5). We can then factor out this common factor, resulting in a simplified expression.

Summary & Key Takeaways

• Factor by grouping is necessary when there is no common factor across all terms in the expression.

• Group terms with common factors together to simplify the expression.

• Factor out the common factors from each group and look for any further simplifications.