Question

In the expression \(4 x^2+6\), which quantity is a coefficient? A. 4 B. \(x\) C. 2 D. 6

Short answer

A. 4

Step-by-step solution

Understand the Terms

In the expression, each part separated by a plus or minus sign is called a term. In the expression given, the terms are \(4x^2\) and \(6\).

Identify the Coefficient

A coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression. For example, in \(4x^2\), \(4\) is the coefficient.

Examine Each Term

Look at \(4x^2\). The \(x^2\) is the variable part and \(4\) is the numerical factor, which is the coefficient. Next, look at \(6\), which does not have a variable, so it is a constant, not a coefficient.

Select the Correct Option

From the choices given (A: 4, B: \(x\), C: 2, D: 6), only option A (4) is a coefficient.

Key concepts

algebraic expressions

Algebraic expressions are combinations of variables, numbers, and operations. They are the foundation of algebra and are used to describe mathematical relationships. Each algebraic expression is made up of terms that are separated by addition or subtraction signs.
For instance, in the expression 4x^2 + 6, you have two terms:

• 4x^2
• 6

These terms are separated by a plus sign.
Understanding the component parts of algebraic expressions helps in solving equations and inequalities. It allows us to simplify complex relationships and identify patterns in mathematical problems.

identifying coefficients

A coefficient is the numerical part of a term containing a variable. It's the number that you multiply by the variable. In the context of algebra, coefficients play an essential role because they tell us how many times to include the variable.
For example, in the term 4x^2, the coefficient is 4. It tells us that we have 4 groups of x^2.
To identify coefficients:

• Look for numbers directly in front of variables.
• Ignore the variable and its exponent when identifying the coefficient.

As seen in the exercise, in 4x^2 + 6, only 4x^2 has a coefficient, which is 4. The 6 is a constant, not a coefficient.
Recognizing coefficients is crucial for understanding and simplifying algebraic expressions.

terms in algebra

In algebra, a term is a single mathematical expression. It can be a number, a variable, or a product of numbers and variables. Terms are the building blocks of algebraic expressions.
For example, in the expression 4x^2 + 6:

• 4x^2
• 6

Both of these are terms.
The key to identifying terms is to look for parts of the expression separated by plus or minus signs.
Here are a few quick tips:

• A constant term is a term without a variable (like 6 in the exercise).
• A variable term is a term with a variable (like 4x^2).

By understanding terms, you can better manipulate and solve algebraic expressions and equations. This foundational concept is essential for progressing in algebra.