Problem 43 Factor out the greatest common f... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 10: Problem 43

Factor out the greatest common factor. $$5 y^{3}-15 y^{2}$$

Short Answer

Expert verified

5y^2(y - 3)

Step by step solution

Identify the coefficients and factors

First, look at the coefficients and variables in each term. The terms are 5y^3 and -15y^2.

Find the greatest common factor (GCF)

Identify the GCF of the coefficients (5 and 15). The GCF is 5. For the variables, look for the lowest power of y that appears in both terms, which is y^2.

Factor out the GCF

Factor 5y^2 out of each term: 5y^3 - 15y^2 = 5y^2(y) - 5y^2(3).

Simplify the expression

Combine the factored terms inside the parentheses: 5y^2(y - 3).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Factoring Polynomials

Factoring polynomials is like breaking down numbers into their prime factors. It simplifies expressions by writing them as a product of their factors. In the given exercise, we factor out the greatest common factor (GCF) from the polynomial because it's the largest factor that divides all the terms. Taking our example, 5y鲁 - 15y虏, we notice that both terms share common factors. Simplifying with factoring not only makes equations less complicated but is a crucial skill in algebra, helping in solving and understanding equations.

Coefficients and Variables

Understanding coefficients and variables is key to factoring. Coefficients are numbers multiplied by the variable part; here, 5 and -15 are the coefficients. Variables include the letters (like y) and represent unknown values. For the polynomial 5y鲁 - 15y虏, y is the variable. We look at the coefficients (5 and 15), and variables' powers (y鲁 and y虏). First, we find the GCF of the coefficients, which is 5. Then, we choose the smallest power of the variable present in both terms, which is y虏. This breakdown enables factoring the polynomial efficiently.

Simplifying Expressions

Simplifying expressions involves reducing them to their simplest forms. After factoring out the GCF, the polynomial 5y鲁 - 15y虏 becomes 5y虏(y - 3). This makes solving equations easier and clearer. To simplify, we identify common factors and rewrite the expression by removing these factors. It's like tidying up an equation to make calculations simpler. Simplification is crucial because it reveals the most basic form of an expression, helping us to see relationships and solutions more clearly. Always remember, the goal is to strip down to the simplest, most manageable parts.

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91影视

Factor out the greatest common factor. $$5 y^{3}-15 y^{2}$$

Short Answer

Step by step solution

Identify the coefficients and factors

Find the greatest common factor (GCF)

Factor out the GCF

Simplify the expression

Key Concepts

Factoring Polynomials

Coefficients and Variables

Simplifying Expressions

One App. One Place for Learning.

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