Problem 461 Factor the greatest common facto... [FREE SOLUTION]

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Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 10: Problem 461

Factor the greatest common factor from each polynomial. $$30 u^{2}-10 u$$

Short Answer

Expert verified

$30u^2 - 10u$ factors to $10u(3u - 1)$.

Step by step solution

- Identify the greatest common factor (GCF)

First, find the greatest common factor of the terms in the polynomial. The terms are $30u^2$ and $-10u$. The GCF of 30 and 10 is 10. Each term has at least one $u$, so the GCF is $10u$.

- Factor out the GCF

Rewrite the polynomial by factoring out the $10u$ from each term. Divide each term by $10u$ to determine what remains inside the parentheses: $30u^2 梅 10u = 3u$ $-10u 梅 10u = -1$. Thus, $30u^2 - 10u$ can be factored as $10u(3u - 1)$.

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Key Concepts

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

greatest common factor

To solve polynomial problems more easily, it's essential to understand the greatest common factor (GCF). The GCF is the largest number that can divide each term without a remainder.

For a polynomial like $30u^2 - 10u$, we start by finding the GCF of the numerical parts, 30 and 10. Here, the GCF is 10, because 10 is the highest number that can divide both 30 and 10 evenly.

Next, consider the variable part. Both terms have at least one $u$, so the GCF must also include $u$. Therefore, the total GCF of $30u^2 - 10u$ is $10u$. Finding the GCF helps simplify the polynomial by reducing common factors.

factoring out the GCF

Once we identify the GCF, the next step is to factor it out. Factoring out the GCF means dividing each term in the polynomial by the GCF and placing the GCF outside a parenthesis.

For our example, starting with $30u^2 - 10u$, we know the GCF is $10u$. We divide each term by this GCF, which looks like this:

$30u^2 梅 10u = 3u$
$-10u 梅 10u = -1$

So, $30u^2 - 10u$ can be rewritten as $10u(3u - 1)$. Factoring out the GCF simplifies the polynomial structure and makes it easier to understand and work with.

polynomial simplification

Polynomial simplification makes equations easier to handle and solve. By factoring out the GCF, we reduce complex expressions into simpler forms.

Simplifying $30u^2 - 10u$ using the GCF, we get: $10u(3u - 1)$. This simplified form is more manageable, showing the polynomial's structure clearly and making further operations, like addition, subtraction, or division, more straightforward.

Generally, the simplification process involves these steps:

Identify the GCF of the terms.
Factor out the GCF.
Rewrite the polynomial in its simplified form.

Polynomial simplification saves time and effort, especially when solving more extensive problems or performing further algebraic manipulations.

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91影视

Factor the greatest common factor from each polynomial. $$30 u^{2}-10 u$$

Short Answer

Step by step solution

- Identify the greatest common factor (GCF)

- Factor out the GCF

Key Concepts

greatest common factor

factoring out the GCF

polynomial simplification

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