Exponents and Polynomials Chapter Ten

Adding and Subtracting Polynomials Section 10.1

Polynomial A polynomial in x is a finite sum of terms of the form, where a is a real number and n is a whole number. For example, This polynomial is written in descending powers of x because the powers of x decrease from left to right. Recall that the term 6 can be thought of as. On the other hand, is not a polynomial because one of the exponents is a negative number which is not a whole number. 3

Types of Polynomials b A monomial is a polynomial with exactly one term. b A binomial is a polynomial with exactly two terms. b A trinomial is a polynomial with exactly three terms. 4 Martin-Gay, Prealgebra, 5ed

Adding Polynomials To add polynomials, use the commutative and associative properties and then combine like terms. Add: Remove parentheses. Combine like terms. Simplify. 5

to subtract a polynomial, add its opposite. a - b = a + (-b) Recalling the definition of subtraction, Subtracting Polynomials To subtract two polynomials, change the signs of the terms of the polynomial being subtracted, and then add. 6 Martin-Gay, Prealgebra, 5ed

Subtracting Polynomials... Subtract: Remove parentheses. Combine like terms. Simplify. Add the opposite. Add Change the signs. 7

Helpful Hint Don’t forget to change the sign of each term in the polynomial being subtracted. 8 Martin-Gay, Prealgebra, 5ed