Question

Factor out the GCF. $$ 16 d^{3}+24 d^{2}+32 d $$

   Factor out the GCF.
$$
16 d^{3}+24 d^{2}+32 d
$$

Prealgebra & Introductory Algebra

Prealgebra & Introductory Algebra

Julie Miller, Molly… 2nd Edition

Chapter 13, Problem 20

Instant Answer

Solved by Expert Matthew Biollo

03/27/2021

Step 1

The GCF of the coefficients 16, 24, and 32 is 8. The GCF of the variables $d^3$, $d^2$, and $d$ is $d$. Show more…

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Factor out the GCF. $$ 16 d^{3}+24 d^{2}+32 d $$

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Key Concepts

Polynomial Factorization

Polynomial factorization is the process of breaking down a polynomial into a product of simpler polynomials or factors. This technique, which often begins with factoring out the GCF, is key to solving equations, simplifying expressions, and understanding the structure and roots of polynomial functions.

Greatest Common Factor (GCF)

The greatest common factor is the largest expression, including both numerical coefficients and variable parts, that divides each term of a polynomial without leaving a remainder. It simplifies expressions by removing redundancy and often provides a first step in the process of further factorization or solving equations.

Distributive Property

The distributive property allows you to factor out a common term from each part of an expression. It involves rewriting a sum of terms as a product of the common factor and another expression, effectively reversing the expansion process and simplifying the algebraic expression.

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