(Q22) Sample #1, Math 141/146 common final, long division with polynomials

TL;DR

Learn how to divide polynomials using long division to find the quotient and remainder.

Transcript

number 22 is one of the questions that I like the most we are going to divide the polynomials here we have 4x squared plus 5x plus 4 on the top over X plus 3 and we're going to use long division for this so put a top inside and the X plus 3 the bottom on the outside all right and now this is how we are going to figure out what do we need so in orde... Read More

Key Insights

• 🍉 Polynomial division using long division involves finding the matching leading term and canceling it out before proceeding to the next term.
• 🪘 Subtraction within parentheses during polynomial long division requires careful attention to individual coefficients.
• ➗ The quotient obtained from the long division represents the final result of the division.

Questions & Answers

Q: How do you find the numerator when dividing polynomials using long division?

To find the numerator, you consider the leading term in the divisor and multiply it by the variable to match the leading term of the polynomial being divided. In this case, multiplying 4X by X gives 4X^2, which cancels out the leading term of the polynomial.

Q: What is the significance of canceling out the leading term in long division of polynomials?

Canceling out the leading term helps simplify the division process. By subtracting the polynomial with the matching leading term, it becomes easier to identify the remaining terms and carry out the division for the subsequent terms.

Q: How do you deal with subtraction in polynomial long division?

When subtracting in polynomial long division, it is crucial to pay attention to subtraction within parentheses. Each subtraction is performed term by term, resulting in the evaluation of individual coefficients. Careful execution ensures the correct calculation of the quotient and remainder.

Q: How is the quotient and remainder written in polynomial long division?

The quotient is represented by the polynomial that has been obtained from the long division process. In this case, it is 4X - 7. The remainder, in this case, being 25, is written as a fraction with the remainder on top and the original divisor on the bottom, in this case, X + 3.

Summary & Key Takeaways

• The video explains how to divide the polynomial 4x^2 + 5x + 4 by the binomial x + 3 using long division.

• By considering the leading term, the video demonstrates the process of finding the numerator and cancelling out terms.

• The division is carried out by subtracting the multiplied terms and repeating the process until the quotient and remainder are obtained.