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Chapter 4: Problem 65

Factor each monomial. $$-5 j k$$

Short Answer

Expert verified
The factors of \(-5jk\) are \(-1\), \(5\), \(j\), and \(k\).

Step by step solution

01

Understand the Monomial

A monomial is a mathematical expression consisting of a single term. In this exercise, the monomial we have is \(-5jk\), which consists of a coefficient \(-5\) and two variables \(j\) and \(k\). These elements make up the entire expression.
02

Identify the Factors

To factor the monomial \(-5jk\), determine its individual components. The number \(-5\) is a factor, along with \(j\) and \(k\). Each part is a factor contributing to the product making the monomial.
03

Write the Factors

Compose the factors into a product format. Here, the factors are \(-1\), \(5\), \(j\), and \(k\). Therefore, the factorization of \(-5jk\) is \(-1 \cdot 5 \cdot j \cdot k\). Each component is an individual factor that, when multiplied together, equals \(-5jk\).

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Key Concepts

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

Monomials
Let's talk about monomials. A monomial is a type of algebraic expression that represents a single term. Think of it as a building block in math, consisting of numbers and variables multiplied together.
Monomials are straightforward: they can be a constant, like 7, a variable, like x, or a product of constants and variables, like \(3xy^2\). In our case, the monomial is \(-5jk\). The numbers and letters we see are parts of this single entity known as a monomial.
Factors
Factors are the "pieces" of a monomial. They are elements that multiply together to form the monomial itself.
Every part of a monomial contributes to these factors. For instance, in the expression \(-5jk\), notice that there are different elements at play:
  • \(-1\) and 5 are factors because multiplying them gives us \(-5\).
  • Both \(j\) and \(k\) are variables, acting as separate factors.
To factor a monomial, list out all these individual components! For \(-5jk\), the complete list of factors includes \(-1, 5, j,\) and \(k\). When you multiply them together, they recreate the original expression \(-5jk\).
Algebraic Expressions
Algebraic expressions form the foundation of algebra. They are combinations of numbers, variables, and operation symbols.
An expression could be as simple as a single monomial, or as complex as a polynomial with multiple terms.
Knowing how to navigate these expressions is crucial in algebra, as it allows you to solve problems and understand relationships between numbers.
Our specific expression, \(-5jk\), is a part of this larger world of algebraic expressions. It's vital to recognize the structure of such expressions to simplify, factor, or solve them as needed. Understanding monomials like \(-5jk\) helps build your skills in manipulating algebraic expressions effectively.

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Most popular questions from this chapter

Determine whether the statement is true or false. If true, explain your reasoning. If false, give a counterexample. $$\text { For any integer } a,(-a)^{2}=-a^{2}$$

Find the greatest common factor of each set of numbers or monomials. $$18,28$$

Find each quotient. -50 \div 5

For each expression, use parentheses to group the numbers together and to group the powers with like bases together. Example: \(a \cdot 4 \cdot a^{3} \cdot 2=(4 \cdot 2)\left(a \cdot a^{3}\right)\) $$5 \cdot n^{3} \cdot p \cdot 2 \cdot n \cdot p$$

Simplify each fraction. If the fraction is already in simplest form, write simplified. $$\frac{y^{3}}{y}$$
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