Math Example--Polynomial Concepts--Polynomial Long Division--Example 08

Topic

Polynomials

Description

Determine if (x - 1) is a factor of the polynomial 2x³ - x² - 2x + 1. Divide 2x³ - x² - 2x + 1 by (x - 1) using polynomial long division. Divide 2x³ by x to get 2x², and follow the subtraction and simplification steps. After completing the division, the remainder is 0, which means (x - 1) is a factor of 2x³ - x² - 2x + 1.

Polynomial division is a technique used to divide one polynomial by another, breaking down complex expressions into simpler forms. This collection focuses on examples that illustrate polynomial long division, a method crucial in algebraic manipulation and in understanding factorization and remainder determination.

Seeing multiple worked-out examples is essential for students, as it reinforces the steps involved in polynomial division and provides diverse scenarios that strengthen understanding and confidence.

Teacher’s Script: As we explore polynomial division, let's look at this example. In this case, we are dividing using the divisor provided to see if it’s a factor. Follow each step to observe how terms are divided and remainders calculated. Pay attention to how we align terms and subtract accurately.

For a complete collection of math examples related to Polynomials click on this link: Math Examples: Polynomial Long Division Collection.