Understanding g(3) = 3² – 4(3) + 5 and Why It Equals 2: A Clear Step-by-Step Breakdown

When evaluating expressions like g(3) = 3² – 4(3) + 5, it’s essential to follow the correct order of operations to arrive at the accurate result. This process not only ensures mathematical precision but also enhances understanding of algebraic evaluation—an essential skill in math and STEM education.

In this article, we’ll walk through the step-by-step calculation of g(3) = 3² – 4(3) + 5, explain why evaluating the expression correctly leads to 2, and discuss the importance of following the order of operations (often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).

Understanding the Context

What Does g(3) Mean?

In mathematics, g(x) is a function defined by the expression
g(x) = x² – 4x + 5.
Evaluating g(3) means substituting x = 3 into the function and simplifying accordingly.

g(3) = 3^2 - 4(3) + 5 = 9 - 12 + 5 = 2

Key Insights

Step 1: Substitute x = 3

Start by replacing every instance of x with 3 in the expression:
g(3) = 3² – 4(3) + 5

Step 2: Follow the Order of Operations (PEMDAS)

Now simplify the expression step-by-step:

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Final Thoughts

  1. Evaluate exponents first:
    3² = 9
    So the expression becomes:
    g(3) = 9 – 4(3) + 5

  2. Perform multiplication next:
    4 × 3 = 12
    Now:
    g(3) = 9 – 12 + 5

  3. Carry out subtractions and additions from left to right:

    • First: 9 – 12 = -3
    • Then: -3 + 5 = 2

Final Result:

g(3) = 2

Why This Matters: The Role of Correct Order of Operations

Many students mistakenly perform operations out of sequence—like subtracting before multiplying or adding before multiplying—which leads to incorrect answers. Using PEMDAS ensures consistent, accurate computation, making it indispensable in algebra, calculus, computer science, and engineering.

Moreover, clearly understanding each step enhances mathematical fluency and prepares learners for more complex functions and equations.