If x = -2 and y = 5, what is the value of the algebraic expression \frac{x^3 + 4y}{x + y}? — ACT

If $x = -2$ and $y = 5$ , what is the value of the algebraic expression $\frac{x^3 + 4y}{x + y}$ ?

Answer: 4

Answer

The value of the expression is 4.

Substituting

x = -2

and

y = 5

yields

(-2)^3 + 4(5) = -8 + 20 = 12

in the numerator, and

-2 + 5 = 3

in the denominator. Dividing

12

3

gives

4

Step-by-Step Solution

Substitute the given numerical values into the algebraic expression.

\frac{(-2)^3 + 4(5)}{(-2) + 5}

Replace each occurrence of

x

with

-2

and

y

with

5

Evaluate the numerator using order of operations.

-8 + 20 = 12

Calculate

(-2)^3 = -8

and

4(5) = 20

, then add the terms together.

Evaluate the denominator.

-2 + 5 = 3

Add

-2

and

5

Divide the numerator by the denominator.

\frac{12}{3} = 4

Simplify the fraction to get the final integer answer.

Key Concept

Evaluating algebraic expressions requires substituting specific numerical values into the expression and carefully applying the order of operations, especially when handling negative numbers raised to powers.

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