Determine the value of the polynomial -2a^2 + 5ab - b^3 under the condition that a = -2 an… — Armed Services Vocational Aptitude Battery (ASVAB)

Determine the value of the polynomial $-2a^2 + 5ab - b^3$ under the condition that $a = -2$ and $b = -3$ . Which of the following represents the correct evaluation?

A
-5
B
65
49Answer
D
73

Answer

The correct answer is found by substituting the variable values, properly applying the exponents to the negative numbers (where

(-2)^2 = 4

and

(-3)^3 = -27

), and adhering to the order of operations to multiply before adding and subtracting.

Step-by-Step Solution

Substitute

-2

for

a

and

-3

for

b

into the given polynomial.

-2(-2)^2 + 5(-2)(-3) - (-3)^3

To prepare the expression for numerical evaluation.

Evaluate the exponential terms, noting that a negative number raised to an even power is positive, and to an odd power is negative.

-2(4) + 5(-2)(-3) - (-27)

The order of operations (PEMDAS) requires resolving exponents before multiplication.

Perform the multiplication operations from left to right.

-8 + 30 - (-27)

The order of operations dictates that multiplication must be completed before addition and subtraction.

Convert the subtraction of a negative into addition and calculate the final sum.

-8 + 30 + 27 = 22 + 27 = 49

This is the final step to find the total value of the polynomial.

Key Concept

Evaluating Algebraic Expressions

Estimated Time:45s

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