Question

Factor out the GCF. $$ 100 a^{5} b^{3}+16 a^{2} b $$

   Factor out the GCF.
$$
100 a^{5} b^{3}+16 a^{2} b
$$

Prealgebra & Introductory Algebra

Prealgebra & Introductory Algebra

Julie Miller, Molly… 2nd Edition

Chapter 13, Problem 28

Instant Answer

Solved by Expert Matthew Biollo

03/27/2021

Step 1

The GCF of the coefficients 100 and 16 is 4. The GCF of the variables a^5 b^3 and a^2 b is a^2 b (since a^2 is the lowest power of a and b is the lowest power of b). Show more…

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Factor out the GCF. $$ 100 a^{5} b^{3}+16 a^{2} b $$

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Key Concepts

Exponent Rules

Exponent rules include principles for multiplying and dividing powers with the same base. These rules are useful when factoring expressions containing variables raised to exponents, as they allow you to determine the largest power of each variable that can be factored out from all terms.

Monomials

Monomials are algebraic expressions that consist of a single term, including a constant coefficient and variables raised to non-negative integer powers. Recognizing the structure of monomials helps in identifying common factors such as coefficients and variable powers across multiple terms.

Polynomial Factoring

Polynomial factoring is the process of rewriting a polynomial as a product of simpler components. Factoring out the GCF is often the first step, making the remaining terms simpler and sometimes revealing further factorization opportunities.

Greatest Common Factor (GCF)

The Greatest Common Factor is the largest expression that divides each term in a mathematical expression without leaving a remainder. In the context of polynomials, this involves finding the highest common numeric factor among the coefficients as well as the highest power of variables that are common across all terms.

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