Adding and Subtracting Polynomials Ch 8-1 Students will be able to classify, add, and subtract polynomials. Adding and Subtracting Polynomials Algebra 1 Foundations, pg 502

Ch 8-1 Students will be able to classify, add, and subtract polynomials. In some cases, you can model a situation with an expression composed of monomials. A monomial is a real number, a variable, or a product of a real number and one or more variables with whole-number exponents. Here are some examples of monomials. 18 z -4x2 2.5xy3 a3 Focus Question How are monomials and polynomials related? Polynomials are formed by adding and subtracting monomials. You can add and subtract two polynomials by combining like terms. Algebra 1 Foundations, pg 502

Ch 8-1 Students will be able to classify, add, and subtract polynomials. The degree of a monomial is the sum of the exponents of its variables. The degree of a nonzero constant is 0. Zero has no degree. What is the degree of each monomial? 5x Degree: ___ 6x3y2 Degree: ___ 4 Degree: ___ 8xy Degree: ___ -7y4z Degree: ___ 11 Degree: ___ Problem 1 1 5 2 Algebra 1 Foundations, pg 502

Ch 8-1 You can add or subtract by adding or subtracting like terms. Students will be able to classify, add, and subtract polynomials. You can add or subtract by adding or subtracting like terms. Problem 2 What is the sum or difference? 3x2 + 5x2 2. 4x3y – x3y 3. -6x4 + 11x4 4. 2x2y4 – 7x2y4 8x2 3x3y 5x4 – 5x2y4 Algebra 1 Foundations, pg 503

Degree of each monomial Students will be able to classify, add, and subtract polynomials. A polynomial is a monomial or sum of monomials. The following polynomial is the sum of the monomials 3x4, 5x2, -7x, and 1. The polynomial shown above is in standard form. Standard form of a polynomial means that the degrees of its monomial terms decrease from left to right. The degree of a polynomial in one variable is the same as the degree of the monomial with the greatest exponent. The degree of 3x4 + 5x2 – 7x + 1 is 4. 3x4 + 5x2 - 7x + 1 Degree of each monomial 4 2 1 0 Algebra 1 Foundations, pg 503

Name Using Number of Terms Ch 8-1 Students will be able to classify, add, and subtract polynomials. You can name a polynomial based on its degree or the number of monomials it contains. Polynomial Degree Name Using Degree Number of Terms Name Using Number of Terms 6 5x + 9 4x2 + 7x + 3 2x3 8x4 – 2x3 + 3x 0 constant 1 monomial 1 linear 2 binomial 2 quadratic 3 trinomial 3 cubic 1 monomial 4 4th degree 3 trinomial Algebra 1 Foundations, pg 503

Ch 8-1 Students will be able to classify, add, and subtract polynomials. Problem 3 Write each polynomial in standard form. What is the name of the polynomial based on its degree and number of terms? 3x + 4x3 2. 4x – 1 + 5x2 + 7x 3. 2x – 3 + 8x3 4x3 + 3x 5x2 + 4x + 7x – 1 Degree is 3 and 2 terms Degree is 2 and 3 terms Cubic binomial Quadratic trinomial 8x3 + 2x – 3 Degree is 3 and 3 terms Cubic trinomial Algebra 1 Foundations, pg 503

Ch 8-1 You can add polynomials by adding like terms. Problem 4 Students will be able to classify, add, and subtract polynomials. You can add polynomials by adding like terms. Problem 4 Adding polynomials. Algebra 1 Foundations, pg 504

Ch 8-1 Students will be able to classify, add, and subtract polynomials. Recall that subtraction means to add the opposite. So when you subtract a polynomial, change each of the terms to its opposite. Then add the coefficients. Problem 5 Subtracting polynomials. Algebra 1 Foundations, pg 505