1 ALGEBRA 1 Adding and Subtracting Polynomials Mr. J. Grossman

2 VARIABLE EXPRESSIONS A variable expression contains one or more variables. A variable expression contains one or more variables. There is not an equal (=) sign. There is not an equal (=) sign.

3 TERMS The terms are the variables, numbers or combinations of variables and numbers that make up the expression. The terms are the variables, numbers or combinations of variables and numbers that make up the expression. There are 4 terms in the given expression. There are 4 terms in the given expression. Variable terms contain variables. Variable terms contain variables. There are 3 variable terms in the given expression. What are they? There are 3 variable terms in the given expression. What are they? Constant terms contain only numbers. Constant terms contain only numbers. There is 1 constant term in the given expression. What is it? There is 1 constant term in the given expression. What is it?

4 NUMERICAL COEFFICIENT  Each term contains two parts: 1. The variable part and 2. The numerical coefficient  The numerical coefficient is often called simply the coefficient.  It is the number that multiplies (sits in front of) the variable(s).  There is always a number in front of a variable.  If you don’t see a number, then the number is 1.

5 LIKE TERMS Terms that are identical in the variable part (to include exponent value) are like terms. Terms that are identical in the variable part (to include exponent value) are like terms.  Note: Like signs are different from like terms. Constant terms are like terms because they have no variable part and are therefore alike in the variable part. Constant terms are like terms because they have no variable part and are therefore alike in the variable part.

6 COMBINING LIKE TERMS Combine or simplify like terms by adding or subtracting their numerical coefficients. Combine or simplify like terms by adding or subtracting their numerical coefficients. Rearrange the terms if necessary. Use the sign rules correctly.

7 Classifying Polynomials Monomial: an expression that is a number, a variable, or the product of a number and one or more variables. Monomial: an expression that is a number, a variable, or the product of a number and one or more variables. a number: 8, a number: 8, a variable: x, or a variable: x, or a product of numbers and variables: 8xy a product of numbers and variables: 8xy Binomial: Binomial: a polynomial with two terms: 2x + 3 a polynomial with two terms: 2x + 3

8 Classifying Polynomials Trinomial Trinomial a polynomial with three terms a polynomial with three terms Polynomial Polynomial a variable expression in which the terms are monomials: a variable expression in which the terms are monomials: 5x + 9y – xy

9 Classifying Polynomials Standard Form of a Polynomial Written in descending order Written in descending order Arranging the terms of a polynomial, according to the exponents, in order from largest to smallest. Arranging the terms of a polynomial, according to the exponents, in order from largest to smallest. Degree of a Polynomial Degree of a Polynomial The degree of the term with the largest degree The degree of the term with the largest degree

10 Classifying Polynomials Constant – a polynomial of 0 degree Constant – a polynomial of 0 degree Linear – a polynomial of 1 degree Linear – a polynomial of 1 degree Quadratic – a polynomial of 2 degree Quadratic – a polynomial of 2 degree Cubic – a polynomial of 3 degree Cubic – a polynomial of 3 degree

11 Classifying Polynomials PolynomialDegree Name Using Degree Nr of Terms Name Using Nr of Terms 1Linear2Binomial 2Quadratic3Trinomial 3Cubic1Monomial 0Constant1Monomial

12 ADDITION & SUBTRACTION OF POLYNOMIALS Add or subtract polynomials by combining like terms. Add or subtract polynomials by combining like terms. Add or subtract their coefficients Add or subtract their coefficients

13 ADDITION & SUBTRACTION OF POLYNOMIALS Add or subtract polynomials by combining like terms. Add or subtract polynomials by combining like terms. Add or subtract their coefficients Add or subtract their coefficients

14 ADDITION & SUBTRACTION OF POLYNOMIALS The minus sign touching the parenthesis of the second polynomial means that a negative one is multiplied by the second polynomial. The minus sign touching the parenthesis of the second polynomial means that a negative one is multiplied by the second polynomial. Perform multiplication before addition. Perform multiplication before addition.

15 ADDITION & SUBTRACTION OF POLYNOMIALS Remove each polynomial from parenthesis, then add Remove each polynomial from parenthesis, then add

16 ADDITION & SUBTRACTION OF POLYNOMIALS Polynomials in more than one variable are added and subtracted by combining like terms. Polynomials in more than one variable are added and subtracted by combining like terms.

17 ADDITION & SUBTRACTION OF POLYNOMIALS Any questions???

18 ADDITION & SUBTRACTION OF POLYNOMIALS Let’s Practice Text pg 459 Problems 1, 9, 15, 21, 28, 35, 39, 40.