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Difficulty: MediumEvaluating Algebraic Expressions

A technician calculates a load factor using the expression x2−2yx+2\frac{x^2 - 2y}{x + 2}. If the inputs are x=−4x = -4 and y=3y = 3, what is the resulting load factor?

  1. A
    -21
  2. B
    -11
  3. -5Answer
  4. D
    11

Answer

The resulting load factor is -5.
Substituting x=−4x = -4 and y=3y = 3 into the numerator gives (−4)2−2(3)=16−6=10(-4)^2 - 2(3) = 16 - 6 = 10. Substituting x=−4x = -4 into the denominator gives −4+2=−2-4 + 2 = -2. Finally, dividing the numerator by the denominator yields 10/−2=−510 / -2 = -5.

Step-by-Step Solution

1
Substitute the values x=−4x = -4 and y=3y = 3 into the numerator of the expression.
(−4)2−2(3)(-4)^2 - 2(3)
Variable substitution requires replacing the letters with their corresponding numerical values, using parentheses for negative numbers.
2
Evaluate the numerator following the standard order of operations.
16−6=1016 - 6 = 10
Squaring the negative integer −4-4 results in positive 1616. Multiplication (2×3=62 \times 3 = 6) must be performed before subtraction.
3
Substitute the value of xx into the denominator and evaluate.
−4+2=−2-4 + 2 = -2
Adding a positive integer to a negative integer reduces its absolute value while maintaining the negative sign.
4
Divide the evaluated numerator by the evaluated denominator.
10/−2=−510 / -2 = -5
A positive number divided by a negative number results in a negative quotient.

Key Concept

Evaluating rational algebraic expressions with negative integers
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Topics

Evaluating Algebraic Expressions

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