In Exercises 23–34, factor out the negative of the greatest common factor. −4x³ + 32x² − 20x

Key Concepts

Greatest Common Factor (GCF)

The Greatest Common Factor (GCF) is the largest integer or algebraic expression that divides each term of a polynomial without leaving a remainder. To find the GCF, identify the common factors in the coefficients and the variables of each term. For example, in the expression -4x³ + 32x² - 20x, the GCF is 4x, as it is the highest factor that can be factored out from all terms.

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial as a product of its factors. This process simplifies expressions and can make solving equations easier. In the context of the given polynomial, factoring out the GCF helps to express the polynomial in a simpler form, which can be useful for further analysis or solving.

Negative Sign in Factoring

Factoring out a negative sign means extracting a negative value from the polynomial, which can change the signs of the terms. This is particularly useful when the leading coefficient is negative, as it can help to standardize the expression. In the given polynomial, factoring out the negative of the GCF will result in a polynomial with positive leading coefficients, making it easier to work with.