2.1 Sums and Differences of Polynomials

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Presentation transcript:

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

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

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

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

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

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

Simplify. 3. 4.

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

To simplify these expressions you can add the like terms 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

A + B B – C C – A A + C - B

Questions 9-10: Simplify. 9. 10.

2.2 Solving Equations

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

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