If n = 4, what is the value of n^2 + 3n - 2?14182630

1. TRANSLATE the problem information

• Given information: \(\mathrm{n = 4}\)
• Find: The value of \(\mathrm{n^2 + 3n - 2}\)
• What this tells us: We need to replace every "n" in the expression with the number 4

2. SIMPLIFY through substitution and calculation

• Replace n with 4: \(\mathrm{(4)^2 + 3(4) - 2}\)
• Apply order of operations:
  • First, calculate the exponent: \(\mathrm{(4)^2 = 16}\)
  • Next, calculate the multiplication: \(\mathrm{3(4) = 12}\)
  • Now we have: \(\mathrm{16 + 12 - 2}\)
• Work from left to right: \(\mathrm{16 + 12 = 28}\), then \(\mathrm{28 - 2 = 26}\)

Answer: C (26)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make arithmetic errors or misapply order of operations.

For example, they might calculate \(\mathrm{3(4) - 2}\) first, getting \(\mathrm{3(2) = 6}\), then add \(\mathrm{16 + 6 = 22}\). Or they might forget to square the 4, treating \(\mathrm{4^2}\) as just 4, leading to \(\mathrm{4 + 12 - 2 = 14}\).

This may lead them to select Choice A (14) or get confused and guess among the options.

The Bottom Line:

This problem tests careful execution of basic algebra skills. While the concept is straightforward, students must methodically follow order of operations and avoid rushing through the arithmetic to avoid careless errors.