# Adding and Subtracting Polynomials

**1. Vocabulary:**

• A variable is a quantity represented by a letter.

• A polynomial is the sum of terms that contain variables raised

to positive integer or zero powers and that have no variables in

any denominator .

• A term is one of the addends in an addition expression . For

example, in the expression 2x + 4, the terms are 2x and 4.

• The parts of each term that are multiplied are the factors of the

term . For example, in the term 2x from the example above, the

factors are 2 and x.

• Like terms have the same variable factors raised to the same

powers . For example, in the expression

2x^2 + 3x + 7 + 3x^2 + 4x + 9, the 2x^2 and 3x^2 are like terms, the

3x and 4x are like terms, and the 7 and 9 are like terms.

**2. Adding Polynomials: **To add two polynomials, use
the

commutative and associative properties of addition to rewrite the sum

so that like terms are grouped , and then use the distributive property

to combine like terms .

**Example 1:** Simplify.

**3. Negating Polynomials: **If there is a negative
sign directly

preceding the parenthesis surrounding a polynomial, the negative

sign applies to each term inside the parenthesis. Use the distributive

property to distribute the negation to each term inside the

parenthesis. You may think of the negative preceding the

parenthesis as a –1, and use the rules for multiplying signed

numbers .

**Example 2:** Simplify.

**4. Subtracting Polynomials : **To subtract two
polynomials, change

the subtraction to addition of the opposite and then add.

Example: Simplify.

**4. Evaluating Polynomials: **To find the value of a
polynomial at a

given value of the variable , substitute the value of the variable into

the polynomial everywhere the variable appears.

**Example:** Evaluate the given polynomial at the given
value of

the variable.

Practice Problems

Simplify each of the following :

Evaluate the given polynomial at the given value of the variable.

Answers to Practice Problems

f. The value of the polynomial is 10.

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