Dividing polynomials 1 | Polynomial and rational functions | Algebra II | Khan Academy

TL;DR

Learn how to perform algebraic long division to divide x squared minus 3x plus 2 by x minus 2.

Transcript

Divide x squared minus 3x plus 2 divided by x minus 2. So we're going to divide this into that. And we can do this really the same way that you first learned long division. So we have x minus 2 being divided into x squared minus 3x plus 2. Another way we could have written the same exact expression is x squared minus 3x plus 2, all of that over x m... Read More

Key Insights

• ➗ Algebraic long division is a method used to divide algebraic expressions.
• 🍉 The highest degree term of the divisor determines the first term of the quotient.
• 🍉 Multiplying the quotient term by the divisor and subtracting it from the dividend gives the next term of the quotient.
• 🍉 The process continues until no more terms can be divided, resulting in the final quotient.
• 🪘 Algebraic long division is similar to traditional long division but applied to algebraic expressions.
• ✖️ The process involves multiplication, subtraction, and addition to find the quotient.
• 😑 The final quotient can be verified by multiplying it with the divisor to check if the original expression is obtained.

Questions & Answers

Q: How do you perform algebraic long division?

Algebraic long division is performed by considering the highest degree term of the divisor and the dividend and then finding the quotient term by term through multiplication and subtraction.

Q: What is the first step in algebraic long division?

The first step is to compare the highest degree term of the divisor and dividend. In this case, it is x squared and x. x goes into x squared once, so the first term of the quotient is x.

Q: How do you multiply x times x minus 2?

To multiply x times x minus 2, you distribute x to both terms: x times x is x squared, and x times -2 is -2x.

Q: What is the final quotient in this example?

The final quotient is x minus 1 when you divide x squared minus 3x plus 2 by x minus 2.

Summary & Key Takeaways

• The video explains the process of performing algebraic long division to divide x squared minus 3x plus 2 by x minus 2.

• The highest degree term on x minus 2 is x, and on x squared minus 3x plus 2 is x squared. x goes into x squared once.

• Multiply x times x minus 2 to get x squared minus 2x. Subtract this from x squared minus 3x plus 2 to get -x plus 2.

• x minus 2 goes into -x plus 2 once, resulting in x minus 1 as the final quotient.