Dividing quadratics by linear expressions with remainders | Algebra 2 | Khan Academy

TL;DR

Learn how to simplify a polynomial division problem by using algebraic long division.

Transcript

• [Instructor] So if you've been watching these videos, you know that we have a lot of scenarios where people seem to be walking up to us on the street and asking us to do math problems. And I guess this will be no different. So let's say someone walks up to you on the street and says, "Quick, you, "x squared plus five x plus eight over x plus two,... Read More

Key Insights

• ➗ Simplifying polynomial division can be done by factoring the numerator or using algebraic long division.
• 🧑‍🏭 Factoring the numerator helps identify common factors with the denominator.
• 🍉 Algebraic long division involves dividing the numerator term-by-term and subtracting the product from the original numerator.

Questions & Answers

Q: What are the two methods discussed for simplifying polynomial division?

The two methods discussed are factoring the numerator and using algebraic long division.

Q: How do you factor the numerator to simplify polynomial division?

To factor the numerator, you look for two numbers that add up to the coefficient of the x term and multiply to the constant term. In this case, x + 2 is a factor of the numerator.

Q: How does algebraic long division work for polynomial division?

Algebraic long division involves dividing the numerator by the denominator term-by-term. You start with the highest degree terms and divide them. Then, you subtract the product from the original numerator and bring down the next term. Repeat the process until no more terms can be divided.

Q: What happens if there is a remainder in polynomial division?

If there is a remainder, it is written as a fraction with the remainder as the numerator and the denominator as the original denominator. In this case, the remainder is 2, so the simplified expression is x + 3 with a remainder of 2.

Summary & Key Takeaways

• This video teaches two methods for simplifying polynomial division: factoring the numerator and using algebraic long division.

• The first method involves factoring the numerator to check for common factors with the denominator.

• The second method, algebraic long division, involves dividing the numerator by the denominator step-by-step to simplify the expression.