The 3rd Degree Polynomial calculator computes a answer (y) to third degree polynomial where a, b, c, and d are each multiplicative constants and x is the independent variable.
INSTRUCTIONS: Enter the following:
3rd Degree Polynomial (y): The calculator returns the value of y.
A third degree polynomial is an equation of the form:
`y = ax^3 +bx^2 + cx + d` (showing the multiplications explicitly: `y = a*x^3 +b*x^2 + c*x + d`)
In this simple algebraic form there are four additive terms shown on the right of the equation:
The equation is called "third degree" because it has an `x^3` term. If it also had an `x^4` term in it, it would be called a fourth degree polynomial.
Note that the four terms could be thought of as each term having a multiplying constant: a, b, c, and d
So, the form of the third degree polynomial could be re-written more explicitly to be:
`y = a*x^3 + b*x^2 + c*x^1 + d*x^0`
We can make up examples values of a, b, c, and d to form an infinite number of variations on a third degree polynomial. The multiplicative constants, a, b, c, and d, can have integer or decimal values:
ex. `y = 5x^3 + 6x^2 + 7x + 23` ; if `x = 5`, this evaluates to `y = 833`
ex. `y = 3.7x^3 + 2.1x^2 + 0.4x + 22.2` ; if `x = 4.5`, this evaluates to `y = 403.6875`
The multiplicative constants for b, c and d can also be zero. Technically, the a constant can't be zero if the equation is to be called a "third degree polynomial" but this brings up an interesting point: a lower degree polynomial is only a higher degree polynomial with all the higher order terms having multiplicative constants equal to zero. `a*x^3 + b*x^2 + c*x + d = 0*x^5 + 0*x^4 + a*x^3 + b*x^2 + c*x + d`
Here are two examples of the b, the c, or the d constants being zero.
Here is an example of one of the constants, the c constant, being a negative multiplier:
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