A polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial in a single indeterminate, x, can be written in the form:
P(x) = anxn + an-1xn-1 + ... + a1x + a0
Here:
x is the variable.
an, an-1, ..., a1, a0 are the coefficients, which are constants.
n is a non-negative integer, representing the degree of the polynomial (the highest exponent of the variable).
anxn is a term, where an is the coefficient and xn is the variable part.
This calculator helps you evaluate a polynomial for a given value of x. You provide the coefficients of the polynomial in order from the highest degree term to the constant term, and the specific value of x you want to test. The calculator then computes the result of the polynomial expression.
How it Works:
The calculator takes your input for the coefficients and the value of x. It then iterates through each coefficient, multiplies it by x raised to the appropriate power (starting from the highest degree), and sums up all these term values to give you the final result of P(x).
If you enter 2,-5,3,-7 into the "Polynomial Coefficients" field and 4 into the "Value of x" field, the calculator will output 53.
Use Cases:
Polynomial evaluation is a fundamental operation in many areas of mathematics, science, and engineering, including:
Root Finding: Determining the values of x for which P(x) = 0.
Curve Sketching: Understanding the behavior of functions.
Interpolation: Fitting a polynomial to a set of data points.
Computer Graphics: Used in Bezier curves and other shape representations.
Numerical Analysis: Approximating complex functions with polynomials.
function evaluatePolynomial() {
var coefficientsInput = document.getElementById("coefficients").value;
var xValueInput = document.getElementById("xValue").value;
var resultValueElement = document.getElementById("resultValue");
resultValueElement.innerHTML = "—"; // Reset previous result
if (!coefficientsInput || !xValueInput) {
alert("Please enter both polynomial coefficients and a value for x.");
return;
}
var coefficientsStr = coefficientsInput.split(',');
var coefficients = [];
for (var i = 0; i < coefficientsStr.length; i++) {
var coeff = parseFloat(coefficientsStr[i].trim());
if (isNaN(coeff)) {
alert("Invalid coefficient found. Please ensure all coefficients are numbers separated by commas.");
return;
}
coefficients.push(coeff);
}
var x = parseFloat(xValueInput);
if (isNaN(x)) {
alert("Invalid value for x. Please enter a valid number.");
return;
}
var result = 0;
var n = coefficients.length – 1; // Degree of the polynomial is one less than the number of coefficients
for (var i = 0; i < coefficients.length; i++) {
var power = n – i;
var termValue = coefficients[i] * Math.pow(x, power);
result += termValue;
}
resultValueElement.innerHTML = "" + result.toFixed(6) + ""; // Display with a few decimal places for precision
}