Simplify the polynomial $(-8 x)+x+(-2 x)$
A) $-5 x$
B) $9 x$
C) $5 x$
D) $-9 x$
Answer (1)
Combine the coefficients of the x terms: − 8 + 1 − 2 = − 9 .
Multiply the result by x : − 9 x .
The simplified polynomial is − 9 x .
The correct option is D) − 9 x , so the final answer is − 9 x .
Explanation
Understanding the Problem We are asked to simplify the polynomial ( − 8 x ) + x + ( − 2 x ) . This involves combining like terms, which means adding the coefficients of the x terms.
Adding the Coefficients To simplify the polynomial, we add the coefficients of the x terms: − 8 + 1 + ( − 2 ) .
− 8 + 1 + ( − 2 ) = − 8 + 1 − 2 = − 7 − 2 = − 9
Multiplying by x Now, we multiply the result by x to get the simplified polynomial: − 9 x .
Choosing the Correct Option Comparing our simplified polynomial − 9 x with the given options, we see that it matches option D.
Final Answer Therefore, the simplified form of the polynomial ( − 8 x ) + x + ( − 2 x ) is − 9 x .
Examples
Polynomials are used in various fields, such as physics, engineering, and economics. For example, in physics, polynomials can be used to describe the trajectory of a projectile. In economics, they can be used to model cost and revenue functions. Simplifying polynomials, like in this problem, helps in making these models easier to understand and work with. For instance, if you have a business and your profit is modeled by the polynomial P ( x ) = − 8 x + x − 2 x , where x is the number of items you sell, simplifying it to P ( x ) = − 9 x makes it clear that you are losing money for each item you sell.
