Algebra Unit 3: Factoring Polynomials Quiz

Factoring Polynomials Overview

• 2g² + 5g + 4 is provided as an example of a polynomial that is not completely factored.

Equivalent Expressions

• A student factors 3x² - 12 as 3(x² - 4); this transformation maintains equivalence but is not fully factored.

Methods of Factoring

• For the polynomial 3x³ + 5x + 6x² + 10, the appropriate method is factoring by grouping due to its four terms.
• x² + 12x + 36 is identified as a perfect-square trinomial, indicating a specific factoring approach for three-term polynomials.

Completely Factored Forms

• xy³ - x³y factors to xy(y + x)(y - x), showcasing how variables and polynomial terms can be manipulated.
• The completely factored form of 6x² - 13x - 5 is (2x - 5)(3x + 1), demonstrating the factors of a quadratic expression.
• The expression 2x³ + 4x² - x can be factored as x(2x² + 4x - 1), emphasizing the extraction of common factors.

Special Cases in Factoring

• For the difference of squares, a² - 121 can be factored as (a - 11)(a + 11).

Complete Factor Status

• 3x(9x² + 1) is mentioned as a polynomial that is factored completely, highlighting the end goal of factoring processes.

Completing the Factor

• To make x² - a completely factored, the value of a would be 12, demonstrating how specific values can influence the factorization process.