Question

The weight of a car is modeled with the polynomial x2 + 10x + 200. The weight of a x3 + x + 100. Which polynomial represents the total weight of the car and truck?

Answer 1

The polynomial that represents the total weight of the car and truck is x^3 + x^2 + 11x + 300.

Step-by-step explanation:

The weight of a car and a truck is modeled by two separate polynomials, x2 + 10x + 200 for the car and x3 + x + 100 for the truck. To find the combined weight of both the car and the truck, we must add the two polynomials together.

Here is the calculation for the total weight polynomial:

Add the x3 term from the truck's weight, which has no corresponding term in the car's weight. This remains x3.

Add the x2 term from the car's weight to the truck's weight; however, there is no x2 term in the truck's weight, so this remains x2.

Add the x terms together: 10x (from the car) + x (from the truck) = 11x.

Add the constant terms together: 200 (from the car) + 100 (from the truck) = 300.

Therefore, the polynomial that represents the total weight of the car and truck is x3 + x2 + 11x + 300.

Answer 2

The combined weight of a car and truck is given as the polynomial P(W) = x³ + x² + 11 x + 300

Step-by-step explanation:

The weight of the car is given as:

P(C) = x² + 10 x + 200

The weight of the truck is given as:

P(T) = x³ + x + 100

Now, the combined weight of both vehicles is given as

= Weight of Car P(C) + Weight of Truck P(T)

P(W) = x² + 10 x + 200 + x³ + x + 100

= x³ + x² + (10 x + x)+ (200 + 100)

= x³ + x² + 11 x + 300

⇒ The combined weight of a car and truck is given as the polynomial P(W) = x³ + x² + 11 x + 300