How to Solve Polynomials

A polynomial is an algebraic expression that has more than one term. A polynomial with one term is called a monomial. A polynomial with two terms is called a binomial. A polynomial with three terms is called a trinomial. You can add, subtract, multiply and divide polynomials. The more you practice polynomials the better you will understand how to solve them.

Instructions

Add Polynomials

1. Add polynomials by aligning like terms vertically.

2. Add the columns.

3. Combine like terms and rewrite in descending order. Descending powers means variables get smaller from left to right. Ascending powers mean variables get larger from left to right.

4. Remove the parentheses.

5. Combine like terms and you are done.

Subtract Polynomials

1. Change the subtraction to addition.

2. Remove grouping symbols.

3. Combine like terms vertically and add the columns to complete the problem.

Multipy polynomials

1. Write down the problem and use the FOIL method to solve it. An easy way to remember the FOIL method is first, outer, inner and last.

2. Use the distributive property to get rid of the parentheses. Use the distributive property again to calculate.

3. Combine like terms to complete.

Divide Polynomials

1. To divide polynomial by a monomial divide the bottom number into the top number of the fraction.

2. Use the distributive property.

3. Multiplying by 1/x is the same as dividing by x.

Tips & Warnings

• A few examples of a polynomial with one variable are -2x, 8 or 3x.

• Subtract polynomials the same way you subtract signed numbers.

• You add the additive inverse of the polynomial being subtracted to the polynomial to the polynomial you are subtracting from.

• To find the additive inverse of a polynomial, change all the signs of the polynomial or by multiply the polynomials by a negative 1 or (-1).

• In multiplying polynomials, you will use the distributive property more than one time. You use the distributive property to remove the parenthesis. Then you use it again to calculate.

• Dividing a polynomial by a monomial is accomplished by dividing each term of the polynomial by the monomial.