2 1 Sums and Differences of Polynomials Goals

2. 1 Sums and Differences of Polynomials

Goals § SWBAT simplify expressions for sums and differences of polynomials § SWBAT solve first-degree equations in one variable

Definitions monomial §A is a numeral, a variable, or an indicated product of a numeral and one or more variables. § Example:

Definitions § When looking at the monomial , the number denoted by a is called the coefficient of the variable. § The symbol represents a power of x, where x is called the base exponent and n is called the .

Definitions § A monomial with no variable (i. e. 9 or -6) is constant called a. degree § The of a monomial is the exponent, n. If the monomial contains more than one variable, the degree of the monomial is the of sum the exponents. § Example: What is the degree of What is the coefficient? ?

Definitions § A monomial or sum of monomials is called a polynomial. § The monomials of the expression are called the terms of the polynomial. The coefficients on each term of the polynomial are called the coefficients of the polynomial. degree § The of a polynomial is the degree of the term with the highest degree.

State the coefficients and the degree of each polynomial. 1. 5, -9, 6, -22 Degree: 7 2. 3, -9 Degree: 6

Definitions like § Two monomials are said to be terms if they have the same variable(s) with the same exponent(s) and their only difference is their coefficient. binomial § A is a polynomial with two trinomial terms. A is a polynomial with three terms. Example: Binomial: Trinomial: § When simplifying a polynomial expression, combine the like terms by adding or subtracting their coefficients.

Simplify. 3. 4.

Given the two polynomials: and § this is the polynomials. sum of the polynomials difference of the

§ To simplify these expressions you can add the like terms. If it is a subtraction problem, distribute the negative and then combine the like terms.

Questions 5 -8: Find the sum or difference and write the answer in simplest form. Let

Questions 9 -10: Simplify. 9. 10.

2. 2 Solving Equations

§ To solve an equation we can transform the equation into an equivalent equation to get the solution.

Ways to Transform and Solve an Equation: 1. Substituting for either side of the given equation an expression equivalent to it. 2. Adding to or subtracting from each side of the given equation. 3. Multiplying or dividing each side of the equation by the same nonzero number. *This also includes multiplying by a reciprocal*

§ Make sure when transforming equation to only combine terms! like

Solve the equation. 1.

Solve the equation. 2.

Solve the equation. 3.

Your turn! Solve #4 -6

Solve the equation. 7.

Solve the equation. 8.

Solve for the variable indicated. 9. Solve for n.

Solve for the variable indicated. 10. Solve for x