Divide using Long Division (2x^4 - 3x^2 + 6x)/(x - 3) MyMathlab Homework

TL;DR

Learn how to divide polynomials using long division with a step-by-step explanation and examples.

Transcript

divide using long division so we have 2x to the fourth minus 3x squared plus 6x over X minus 3 the first thing you want to do is write this piece on the outside so X minus 3 and the top piece goes on the inside so we have 2x to the fourth notice you're missing an x cubed here so you want to add a zero X cubed so you put that in here a zero X cubed ... Read More

Key Insights

• ➗ Long division is a method used to divide polynomials and involves several steps of multiplication and subtraction.
• 🍉 Placeholders are helpful tools in aligning terms properly during the division process.
• ❓ The quotient, remainder, and divisor are essential components that make up the solution.
• 🤘 Paying careful attention to signs is crucial to avoid errors during subtraction.
• 🪘 Long division of polynomials can be complex and requires precision to obtain the correct solution.
• 😑 Dividing polynomials helps in simplifying expressions and solving algebraic problems.
• ➗ Understanding the process of long division is essential for mastering polynomial division.

Questions & Answers

Q: What is the purpose of using placeholders in long division of polynomials?

Placeholders are used to ensure that all terms are aligned properly during the division process. They help in adding missing terms and simplifying calculations.

Q: How do you determine what to multiply by X in each step of long division?

To find the term to multiply by X, you ask yourself what term, when multiplied by X, will result in the next term of the dividend. This step ensures that the division is carried out correctly.

Q: What happens when the coefficients of the terms being subtracted from the dividend have opposite signs?

When subtracting terms with opposite signs, it results in a sum with a positive sign. This is because subtracting a negative number is equivalent to adding the positive value.

Q: How is the solution written when dividing polynomials using long division?

The solution is written in the form of the quotient plus the remainder over the divisor. This form represents the division of polynomials accurately.

Summary & Key Takeaways

• This video provides a detailed demonstration of dividing polynomials using long division.

• The process involves adding placeholders for missing terms and performing multiple multiplication and subtraction steps.

• The quotient, remainder, and divisor are key components when dividing polynomials.