Example of Addition of Polynomials

The polynomials are expressions algebraic with more than three terms which can no longer be reduced to each other, for example: 2w + 5x + 3y - z. Like all mathematical values, polynomials can participate in operations such as addition. To correctly calculate a sum of polynomials, there are a number of conditions:

• Must be identify like terms. For example: (3x, 2x) are similar because they both have the "x" and can be added like this: 3x + 2x = 5x.
• Must take a good look at the exponents that each term has. For example: if we have (3x², 2x, 2x², 4x) in a sum, we should note that the “x²"Are different from" x ". They are indicated like this: (3x² + 2x²) + (2x + 4x); the "x²"With the" x²", And the" x "with the" x ". The result is expressed: 5x² + 6x.

To solve a sum of polynomials, three steps are followed:

• Group like terms
• Add like terms
• Order the terms of the result alphabetically and by exponents

Example of sum of polynomials

The polynomials to be added are:

(x⁴ + 3x³ + 2x² + 6x + 9) + (x⁵ - 8x³ + 4x² + 12) + (2x⁶ + 3x⁴ - Y³ + 6y² + and - 6)

Group like terms

The terms that have the same variable are put together:

2x⁶ + x⁵ + (x⁴ + 3x⁴) + (3x³ - 8x³) - Y³ + (2x² + 4x²) + 6y² + 6x + y + (9 + 12 - 6)

Like terms are written in parentheses. After that, we are going to add them among them.

Add like terms

2x⁶ + x⁵ + (x⁴ + 3x⁴) + (3x³ - 8x³) - Y³ + (2x² + 4x²) + 6y² + 6x + y + (9 + 12 - 6)

2x⁶ + x⁵ + (4x⁴) + (- 5x³) - Y³ + (6x²) + 6y² + 6x + and + (15)

Like terms have been added, respecting the signs within the parentheses. Now, the parentheses are going to be removed, to leave the resulting signs.

2x⁶ + x⁵ + 4x⁴ - 5x³ - Y³ + 6x² + 6y² + 6x + and + 15

Order the terms of the result alphabetically and by exponents

The terms have already been ordered according to their exponents. Since we have x, y, first the "x" will go and then the "y". Remains:

2x⁶ + x⁵ + 4x⁴ - 5x³ - Y³ + 6x² + 6y² + 6x + and + 15

This is the result of the sum of the polynomials, and it can no longer be reduced to fewer terms.

Now you know how to correctly solve a sum of polynomials.

Keep reading at:

• Examples of Polynomials