Problem 439 Find the greatest common factor.... [FREE SOLUTION]

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Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 10: Problem 439

Find the greatest common factor. $$35 x^{3}, 10 x^{4}, 5 x^{5}$$

Short Answer

Expert verified

The GCF is $5x^3$.

Step by step solution

Identify the coefficients

List the coefficients of each term: 35, 10, and 5.

Find the GCF of the coefficients

Determine the greatest common factor (GCF) of 35, 10, and 5, which is 5.

Identify the variables

List the variable part of each term: $x^3$, $x^4$, and $x^5$.

Find the lowest power of the variable

The lowest power of the variable among $x^3$, $x^4$, and $x^5$ is $x^3$.

Combine the GCF of coefficients and the lowest power of the variable

Multiply the GCF of the coefficients (5) by the lowest power of the variable ($x^3$). The GCF of the terms is $5x^3$.

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Key Concepts

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

Coefficients

Coefficients are numbers that are placed before variables in algebraic expressions. In the original problem, the coefficients are the numbers in front of the variable 'x' in each term: 35, 10, and 5. After identifying the coefficients, the next step is to find their greatest common factor (GCF). The GCF is the largest number that can divide each coefficient without leaving a remainder. In this case, the GCF of 35, 10, and 5 is 5.

First, identify and list all the coefficients in your problem.
Second, determine the largest number that divides all the coefficients.

Variables in Algebra

Variables in algebra are symbols, usually letters, that represent numbers. In our problem, the variable is 'x'. Each term has 'x' raised to different powers: 35x鲁, 10x鈦�, and 5x鈦�.

Identify the variable present in each term.
List the powers of the variable from each term. Here, they are 3, 4, and 5.
Find the lowest power of the variable.

The lowest power of 'x' among 3, 4, and 5 is 3. This lowest power is a key part of determining the greatest common factor.

Exponents

Exponents indicate how many times a number or variable is multiplied by itself. In our exercise, each term includes 'x' raised to an exponent: 3, 4, and 5. Here's a quick breakdown:

The exponent in 35x鲁 is 3, meaning x is multiplied by itself three times: x * x * x.
The exponent in 10x鈦� is 4, so x is multiplied by itself four times: x * x * x * x.
The exponent in 5x鈦� is 5, meaning x is used five times: x * x * x * x * x.

To find the GCF of the variable part, we use the lowest exponent. For 'x' in this problem, that is 3. Thus, 'x鲁' becomes part of our final greatest common factor. Combining the GCF of the coefficients (5) and the lowest power of the variable (x鲁), we get 5x鲁 as the answer.

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91影视

Find the greatest common factor. $$35 x^{3}, 10 x^{4}, 5 x^{5}$$

Short Answer

Step by step solution

Identify the coefficients

Find the GCF of the coefficients

Identify the variables

Find the lowest power of the variable

Combine the GCF of coefficients and the lowest power of the variable

Key Concepts

Coefficients

Variables in Algebra

Exponents

One App. One Place for Learning.

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