More examples of factoring by grouping | Algebra I | Khan Academy

TL;DR

Learn how to factor quadratic polynomials with leading coefficients other than 1 using the technique of factoring by grouping.

Transcript

In this video, I want to focus on a few more techniques for factoring polynomials. And in particular, I want to focus on quadratics that don't have a 1 as the leading coefficient. For example, if I wanted to factor 4x squared plus 25x minus 21. Everything we've factored so far, or all of the quadratics we've factored so far, had either a 1 or negat... Read More

Key Insights

• 🥺 Factoring by grouping is a technique used to factor quadratic polynomials with non-1 leading coefficients.
• 👥 The technique involves finding two numbers that satisfy specific conditions and splitting the polynomial into two groups.
• 👻 Factoring by grouping allows for the factorization of quadratics into two binomials with a common factor.
• ❓ Factoring by grouping becomes obsolete once the quadratic formula is learned.
• 🧑‍🏭 Factoring out a common binomial is a crucial step in factoring by grouping.
• 🥺 Factoring by grouping simplifies the process of factoring polynomials with non-1 leading coefficients.
• 🥺 Factoring polynomials with non-1 leading coefficients requires considering all possible factor combinations.

Questions & Answers

Q: What is factoring by grouping?

Factoring by grouping is a technique used to factor quadratic polynomials with a leading coefficient other than 1. It involves finding two numbers that satisfy specific conditions and splitting the polynomial into two groups to factor out common terms.

Q: When is factoring by grouping useful?

Factoring by grouping is useful when factoring quadratic polynomials with leading coefficients other than 1. It allows for the factorization of such polynomials into two binomials.

Q: What are the conditions for factoring by grouping?

The conditions for factoring by grouping are finding two numbers whose product is equal to the product of the leading coefficient and the constant term, and whose sum is equal to the coefficient of the middle term.

Q: How do you factor a polynomial using factoring by grouping?

To factor a polynomial using factoring by grouping, first identify two numbers that meet the conditions of the technique. Split the polynomial into two groups based on these numbers. Factor out common terms from each group. Finally, factor out a common binomial from the two groups to obtain the factored form.

Summary & Key Takeaways

• Factoring quadratic polynomials with a leading coefficient that is not 1 can be done using the technique of factoring by grouping.

• To factor such polynomials, find two numbers whose product is equal to the product of the leading coefficient and the constant term, and whose sum is equal to the coefficient of the middle term.

• Split the polynomial into two groups and factor out common terms from each group. Then factor out a common binomial from the two groups.