Question

Two buildings on opposites sides of a highway are 3x^3- x^2 + 7x +100 feet apart. One building is 2x^2 + 7x feet from the highway. The other building is x^3 + 2x^2 - 18 feet from the highway. What is the standard form of the polynomial representing the width of the highway between the two building?

Answer 1

Given:

Distance between two buildings = $3x^3- x^2 + 7x +100$ feet apart.

Distance between highway and one building = $2x^2 + 7x$ feet.

Distance between highway and second building = $x^3 + 2x^2 - 18$ feet.

To find:

The standard form of the polynomial representing the width of the highway between the two building.

Solution:

We know that,

Width of the highway = Distance between two buildings - Distance of both buildings from highway.

Using the above formula, we get the polynomial for width (W) of the highway.

$W=3x^3- x^2 + 7x +100-(2x^2 + 7x)-(x^3 + 2x^2 - 18)$

$W=3x^3- x^2 + 7x +100-2x^2-7x-x^3 -2x^2+18$

Combining like terms, we get

$W=(3x^3-x^3)+(- x^2 -2x^2-2x^2)+ (7x -7x)+(100 +18)$

$W=2x^3-5x^2+0+118$

$W=2x^3-5x^2+118$

Therefore, the width point highway is $2x^3-5x^2+118$.