Project 21: Adding Polynomials

Application:  Suppose two boys decide to throw a rock in the air.  The first boy (Adam) is standing on a platform that is 12 feet off the ground.  The second boy (Blake) is standing on the ground.

The height of Adam's rock can be expressed as:  y = -x^2 +4x + 12  (where x is time in seconds after the throw and y is the height of the rock in feet)

The height of Blake's rock can be expressed as: y = -x^2 + 6x (where x is time in seconds after the throw and y is the height of the rock in feet)

To know how much higher Adam's rock is compared to Blake's rock we could subtract the two polynomials above:

Difference in Height = ( -x^2 +4x + 12 ) - (-x^2 + 6x) 

Simplified this would be written as -x^2 +4x + 12 + x^2 - 6x = -2x + 12

Therefore, the difference in the height of the rocks (Adam's - Blake's) can be expressed as Diff = -2x + 12

Adam's Rock Height:  H = -x^2 +4x + 12  

Blake's Rock Height H = -x^2 + 6x 

Difference = -2x + 12

Explanation:

At X = 0, Adam's rock is at height 12 feet

At X = 0, Blake's rock is at height 0 feet

At X = 0, -2(0) + 12 = 12 which is the difference in the heights (12 - 0)

At X = 2, Adam's rock is at height 16 feet

At X = 2, Blake's rock is at height 8 feet

At X = 2,  -2(2) + 12 = 8 which is the difference in the heights (16- 8)

Webster's Definition of a Polynomial: a mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power (such as a + bx + cx2) 

We can perform operations such as addition, subtract, and multiplication of polynomials.

Example of Polynomial Addition:

(3 + 4x + x^2) + (2 + 3x^2 - 4x^3) = 5 + 4x + 4x^2 - 4x^3

Project 21: Variables 'co' and 'co2' have been initialized.  These arrays represent the coefficients of two polynomials.

Task: To correctly assign the value of an array called 'sum' which corresponds to the sum of the polynomials with coefficients 'co' and 'co2'.

How to add to an array:

x.push(3);

x.push(5);

x.push(4 + 4);

//x would store the array [3,5,8].  The push command adds the value to the end of the array.

Note: If you are coding in Java, you can assume that 'sum' has already been declared and initialized as an empty ArrayList.

**If your code works for 5 test cases, you can enter your e-mail address

Universal Computational Math Methods:

pow(5,2) returns 25.0

abs(-3.0) returns 3

sqrt(49.0) returns 7.0