January 10 Opening Quiz You have 15 minutes

January 10: Opening Quiz You have 15 minutes to solve these 10 equations. 1) 3 x + 6 = 9 6) 2 x - 5 = 1 2) 3 a + 3 = 12 7) 2 c + 4 = 12 3) 3 u + 5 = 20 8) 3 u - 5 = 4 4) 3 z + 5 = 20 5) 2 y - 3 = 1 9) 2 u + 6 = 8 10) 3 b + 4 = 22

Polynomials Defining Polynomials Adding Like Terms

Vocabulary • Monomials - a number, a variable, or a product of a number and one or more variables. 4 x 20 x 2 yw 3 -3, a 2 b 3 3 yz • Polynomials – one or more monomials added or subtracted 4 x + 6 x 2 binomial 20 xy – 4 binomial 3 a 2 - 5 a + 4 trinomial

Like Terms refers to monomials that have the same variable(s) but may have different coefficients. The variables in the terms must have the same powers. Which terms are like? 3 a 2 b, 4 ab 2, 3 ab, -5 ab 2 4 ab 2 and -5 ab 2 are like. Even though the others have the same variables, the exponents are not the same. 3 a 2 b = 3 aab, which is different from 4 ab 2 = 4 abb.

Like Terms Constants are like terms. Which terms are like? 2 x, -3, 5 b, 0 -3 and 0 are like. Which terms are like? 3 x, 2 x 2, 4, x 3 x and x are like. Which terms are like? 2 wx, w, 3 x, 4 xw 2 wx and 4 xw are like.

Adding Polynomials Add: (x 2 + 3 x + 1) + (4 x 2 +5) Step 1: Underline like terms: (x 2 + 3 x + 1) + (4 x 2 +5) Notice: ‘ 3 x’ doesn’t have a like term. Step 2: Add the coefficients of like terms, do not change the powers of the variables: (x 2 + 4 x 2) + 3 x + (1 + 5) 5 x 2 + 3 x + 6

Adding Polynomials Some people prefer to add polynomials by stacking them. If you choose to do this, be sure to line up the like terms! (x 2 + 3 x + 1) + (4 x 2 +5) 5 x 2 + 3 x + 6 Stack and add these polynomials: (2 a 2+3 ab+4 b 2) + (7 a 2+ab+-2 b 2) (2 a 2 + 3 ab + 4 b 2) (2 a 2+3 ab+4 b 2) + (7 a 2+ab+-2 b 2) + (7 a 2 + ab + -2 b 2) 9 a 2 + 4 ab + 2 b 2

Adding Polynomials • Add the following polynomials; you may stack them if you prefer:

Subtracting Polynomials Subtract: (3 x 2 + 2 x + 7) - (x 2 + x + 4) Step 1: Change subtraction to addition (Keep-Change. ). (3 x 2 + 2 x + 7) + (- x 2 + - x + - 4) Step 2: Underline OR line up the like terms and add. (3 x 2 + 2 x + 7) + (- x 2 + - x + - 4) 2 x 2 + x + 3

Subtracting Polynomials • Subtract the following polynomials by changing to addition (Keep-Change. ), then add: