Polynomial Long Division: The Box Method (Area Model)

Описание: Learn a unique and visual approach to polynomial long division: the Box Method (also known as the Area Model)! This video will introduce you to this alternative technique, which some students find more intuitive than traditional long division. We'll go through four detailed examples, including cases with remainders and missing terms, to give you plenty of practice.

The Box Method helps you systematically break down polynomial division by thinking of it like finding the missing side of a rectangle when you know the area (the dividend) and one side (the divisor). You'll see how to set up the box, fill in terms strategically, and determine the quotient and any remainder.

In this video, you'll learn:

Setting up the Box Method: How to arrange the divisor along the side of the box.
Working Backwards: Using the dividend to fill in the box and find the quotient.
Step-by-Step Process:
Determining the first term of the quotient.
Distributing and filling in the box.
Identifying missing terms to complete the dividend.
Continuing the process until all terms are accounted for.
Handling Remainders: How to express the remainder over the divisor in your final answer.
Checking Your Work: Understanding how to multiply the quotient by the divisor (and add the remainder) to get back to the original dividend.
Examples Covered:
1:00 Example 1: (3x³ + 11x² + 11x + 2) / (x + 2) (No Remainder)
4:00 Example 2: (10x³ - 23x² + 16x - 9) / (2x - 3) (With Remainder)
8:30 Example 3: (2x⁴ - x³ + 11x² + 19) / (x² + 3) (Missing Linear Term in Divisor)
12:50 Example 4: (3x⁴ - 4x³ + 12x² + 8x + 3) / (x² - 2x + 5) (Dividing by a Trinomial)
Master polynomial long division using the Box Method! If you found this video helpful, please give it a thumbs up and subscribe to Mario's Math Tutoring for more algebra and precalculus lessons!

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