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Chapter 10: Problem 32

Factor out the greatest common factor. $$5 y-30$$

Short Answer

Expert verified
5(y - 6)

Step by step solution

01

- Identify the GCF

Find the greatest common factor (GCF) of the coefficients of the terms. The coefficients here are 5 and -30. The GCF of 5 and 30 is 5.
02

- Factor the GCF out of each term

Divide both terms by the GCF. This means dividing 5y by 5 and -30 by 5.
03

- Rewrite the expression

After dividing, rewrite the expression in factored form. Original Expression: 5y - 30 Factored Form: 5(y - 6)

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Key Concepts

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

greatest common factor
The greatest common factor (GCF) is the largest number that can divide each of the terms in a polynomial without leaving a remainder.
To find the GCF, we look at the coefficients, which are the numerical parts of the terms in the polynomial.

In the example, the coefficients are 5 and -30. To determine the GCF:
  • List the factors of 5: 1, 5
  • List the factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Identify the largest common factor, which is 5.
Once we find the GCF, we can use it to simplify the polynomial by factoring it out from each term.
prealgebra
Prealgebra often includes learning about factors, greatest common factors (GCF), and basic operations with polynomials.
It's an essential stepping stone to higher-level algebra, where you'll solve more complex equations and understand advanced mathematical concepts.

Understanding how to find the GCF and factor polynomials simplifies many algebraic processes.
  • This skill helps in simplifying expressions.
  • Makes solving equations easier.
In prealgebra, practicing these steps helps build a strong foundation for future math coursework.
factoring techniques
Factoring techniques are methods used to break down polynomials into simpler multiplicative components. The goal is to convert an expression into a product of simpler expressions.

Here are the steps used to factor polynomials, as in the given example:
  • Step 1: Identify the Greatest Common Factor (GCF).
    For 5y - 30, the GCF is 5.
  • Step 2: Divide each term by the GCF.
    For 5y, dividing by 5 gives y. For -30, dividing by 5 gives -6.
  • Step 3: Rewrite the expression.
    Combine the GCF with the simplified terms inside parentheses: 5(y - 6).
This method is straightforward and foundational, making it one of the first techniques students learn in prealgebra to help manage and simplify polynomials.

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Most popular questions from this chapter

Simplify the expression. $$\left(\frac{9 u}{t}\right)^{2}$$

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$$\text { Fill in the blanks }\left(x^{3}\right)^{5}=x \square \cdot \square=x^{15}$$

Simplify. Write the answer with positive exponents only. $$2 x^{-2} y^{-3}$$
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