Question

What is the value of \( (3x^2 - 2x) \) when \( (x = 4) \)?

• A. 40
• B. 50
• C. 52
• D. 60

Hint:

When substituting values, especially negative ones, always use parentheses to avoid errors in calculation, particularly with exponents. For example, if x = -4, \(x^2\) would be \((-4)^2 = 16\), not \(-4^2 = -16\).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
This question requires substituting a given value of a variable into an algebraic expression and evaluating the result by following the order of operations (PEMDAS/BODMAS).
Step 2: Key Formula or Approach
The order of operations is: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Step 3: Detailed Explanation
We are given the expression \(3x^2 - 2x\) and the value \(x = 4\).
Substitute x = 4 into the expression:
\[ 3(4)^2 - 2(4) \] First, evaluate the exponent:
\[ 3(16) - 2(4) \] Next, perform the multiplications:
\[ 48 - 8 \] Finally, perform the subtraction:
\[ 40 \] The calculated value is 40, which corresponds to option (A).
Note: The provided answer key in the document states (C) 52. This is incorrect based on the given expression. The answer 52 would be correct if the expression were \(3x^2 + x\), since \(3(4)^2 + 4 = 48 + 4 = 52\). We proceed with the correct calculation for the question as written.
Step 4: Final Answer
The value of the expression is 40.