Factoring using polynomial division | Algebra 2 | Khan Academy

TL;DR

The video explains how to factor a polynomial equation into linear factors, using a known factor.

Transcript

• [Instructor] We are told the polynomial p of x is equal to four x to the third plus 19 x squared plus 19 x minus six has a known factor of x plus two. Rewrite p of x as a product of linear factors. So pause this video and see if you can have a go at that. All right, now let's work through it together. So if they didn't give us this second piece o... Read More

Key Insights

• 🧑‍🏭 Dividing a polynomial by a known factor can simplify the factoring process.
• 🥺 Factoring by grouping is a technique used for factoring quadratic equations with a non-one leading coefficient.
• 🧑‍🏭 Factoring a polynomial into linear factors allows us to express the polynomial in its most simplified form.
• 🥺 Factoring by grouping involves finding two numbers that multiply to give the product of the leading coefficient and the constant term.
• 🧑‍🏭 Factoring a quadratic equation further allows us to fully factor the original polynomial equation.
• 🧑‍🏭 Factoring a polynomial helps identify its roots or solutions.
• ❓ The process of factoring polynomials requires knowledge of various factoring techniques and algorithms.

Questions & Answers

Q: How does having a known factor make factoring a polynomial easier?

Having a known factor allows us to divide the polynomial and determine the remaining quadratic equation, making the factoring process more straightforward.

Q: What is the purpose of subtracting terms after dividing by the known factor?

Subtracting the terms helps remove the known factor from the polynomial, leaving us with the remaining terms that need to be factored further.

Q: Why do we need to factor a quadratic equation even though we have a linear factor?

Though we have a linear factor, the remaining quadratic equation still needs to be factored as a product of linear factors to fully factor the original polynomial.

Q: What is factoring by grouping, and why is it necessary in certain cases?

Factoring by grouping is a method used to factor quadratic equations with a leading coefficient that is not one. It involves finding two numbers whose product is equal to the product of the leading coefficient and the constant term.

Summary & Key Takeaways

• The video teaches how to rewrite a polynomial equation with a known factor as a product of linear factors.

• By dividing the polynomial by the known factor, the video demonstrates the process of finding the remaining quadratic equation.

• To factor the quadratic equation further, the video suggests using methods such as factoring by grouping.