1 Chapter 5, Section 2 Polynomials

2 A polynomial is a monomial or a sum of monomials. A binomial has TWO unlike terms, and a trinomial has THREE unlike terms. The DEGREE of the polynomial is the same as the highest degree of any monomial in the polynomial. Remember that a monomial is a constant, a variable, or a product of constants and variables; the variables cannot be in the denominator or under a radical.

3 Example 1 Determine if the expression is a polynomial. If so, state the degree of the polynomial: Not a polynomial, because a variable is under a radical sign. Polynomial. 9 th degree

4 Example 2 Simplify (2a 3 + 5a -7) - (a 3 - 3a + 2) Keep Change Change (2a 3 + 5a -7) + (- a 3 + 3a - 2) = 2a 3 + 5a a 3 + 3a - 2 = a 3 + 8a - 9

5 Example 3 Simplify -y(4y 2 + 2y - 3) -y(4y 2 + 2y - 3) = (-y)·4y 2 + (-y)·2y - (-y)·3 = -4y 3 - 2y 2 + 3y

6 Example 4 Simplify (2p + 3)(4p + 1) (2p + 3)(4p + 1) = 2p(4p + 1) + 3(4p + 1) = 8p 2 + 2p + 12p + 3 = 8p p + 3

7 Example 5 Simplify (a 2 + 3a - 4)(a + 2) (a 2 + 3a - 4)(a + 2) = a 2 (a + 2) + 3a(a + 2) - 4(a + 2) = a 3 + 2a 2 + 3a 2 + 6a - 4a - 8 = a 3 + 5a 2 + 2a - 8