Polynomial Calculator

Polynomial Calculator helps to add, subtract, divide and multiply two given polynomials. Polynomials are algebraic expressions that consist of variables, coefficients, constants, whole number exponents and involve arithmetic operation (multiplication, addition, subtraction).

What is Polynomial Calculator?

Polynomial Calculator is an online tool that helps to calculate the result of addition, subtraction, multiplication, and division of two polynomials. Depending upon the number of terms, there are mainly three types of polynomials. These are monomial, binomial and trinomial. To use the polynomial calculator, enter the values in the input boxes.

Polynomial Calculator

How to Use Polynomial Calculator?

Please follow the steps given below to use the polynomial calculator to add, subtract, multiply or divide two polynomials:

• Step 1: Go to Cuemath's online polynomial calculator.
• Step 2: Choose the arithmetic operation from the drop-down list and enter the polynomials in the input boxes.
• Step 3: Click on the "Calculate" button to add, subtract, multiply or divide two polynomials.
• Step 4: Click on the "Reset" button to clear the fields and enter new values.

How Does Polynomial Calculator Work?

When we arrange the terms of a polynomial in descending power of the variable then the polynomial is said to be in standard form. Given below are the methods of applying arithmetic operations to 2 polynomials.

1. Addition

• Write the polynomials in standard form.
• If a polynomial has missing terms, express them with the coefficient "0".
• Add the coefficients of the like terms to get the result.

2. Subtraction

• Write the polynomials in standard form.
• Express the missing terms, if any, by using the coefficient "0".
• Subtract the coefficients of the like terms of the second polynomial from the first to get the result.

3. Multiplication

• Multiply each term of one polynomial with each term of the other polynomial. (On multiplying the variables, x^a and x^b we get x^{a + b}).
• Add the coefficients of the like terms to get the answer.

4. Division

• Usually, the degree of the dividend is greater than the degree of the divisor.
• We can divide any two polynomials by either using long division or synthetic division.

Solved Examples on Polynomial Calculator

Example 1:

Add the two polynomials 2x² + 3x + 5 and 4x - 2. Verify the result using the polynomial calculator.

Solution:

Express the missing terms with the coefficient 0.

Thus 4x - 2 can be written as 0x² + 4x - 2

(2x² + 3x + 5) + (4x - 2) = (2x² + 3x + 5) + (0x² + 4x - 2).

= (2 + 0)x² + (3 + 4)x + (5 - 2)

= 2x² + 7x + 3

Example 2:

Multiply the two polynomials x³ - x + 2 and 3x + 1. Verify the result using the polynomial calculator.

Solution:

(x³ - x + 2) × (3x + 1) = (x³ - x + 2) × (3x) + (x³ - x + 2) × (1)

= 3x⁴ - 3x² + 6x + x³ - x + 2

= 3x⁴ + x³ - 3x² + (6 - 1)x + 2

= 3x⁴ + x³ - 3x² + 5x + 2

Similarly, you can use the polynomial calculator to add, subtract, multiply and divide the following polynomials:

• 9x⁵ + 2x⁴ - 5x - 7 and 2x⁴ + x² + 4
• 4x² + 10x - 1 and 2x - 7

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