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2.1 Sums and Differences of Polynomials

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1 2.1 Sums and Differences of Polynomials

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

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

4 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

5 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

6 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

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

8 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

9 Simplify. 3. 4.

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

11 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.

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

13 A + B B – C C – A A + C - B

14 Questions 9-10: Simplify. 9. 10.

15 2.2 Solving Equations

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

17 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*

18 Make sure when transforming equation to only combine terms!

19 Solve the equation. 1.

20 Solve the equation. 2.

21 Solve the equation. 3.

22 Your turn! Solve #4-6

23 Solve the equation. 7.

24 Solve the equation. 8.

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

26 Solve for the variable indicated.
10. Solve for x

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