Dr Fowler CCM Adding Polynomials Vocabulary Monomials a
Dr. Fowler CCM Adding Polynomials
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, and 3 yz • Polynomials – one or more monomials. • 4 x + 6 x 2, 20 xy - 4, 3 a 2 - 5 a + 4, 8 • Binomial – 2 monomials. Bi = 2 • 4 x + 3, 53 a 2 - a • Trinomial – 3 monomials. Tri = 3 • 4 x + 3 y + 7, 128 a 2 – 4 a + 9
Like Terms have the same letters, and the same exponents. Constants, or “numbers only” are also Like Terms. 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 terms.
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: 5 x 2 + 3 x + 6
2. Add the following polynomials: (3 a 2 + 3 ab - b 2) + (4 ab + 6 b 2) Combine your like terms. 3 a 2 + 7 ab + 5 b 2
Adding Polynomials • Add the following polynomials:
Simplify: x 2 +x+1 + 2 x 2 + 3 x + 2 3 x 2 + 4 x + 3 (4 b 2 + 2 b + 1) + (7 b 2 + b – 3) 11 b 2 + 3 b – 2 3 x 2 – 4 x + 8 + 2 x 2 – 7 x – 5 5 x 2 – 11 x + 3 a 2 + 8 a – 5 + 3 a 2 + 2 a – 7 4 a 2 + 10 a – 12
Adding Polynomials Simplify: (12 y 3 + y 2 – 8 y + 3) + (6 y 3 – 13 y + 5) = 18 y 3 + y 2 – 21 y + 8 (6 x 5 + 3 x 3 – 7 x – 8) + (4 x 4 – 2 x 2 + 9) = 6 x 5+ 4 x 4 + 3 x 3 – 2 x 2 – 7 x + 1
Excellent Job !!! Well Done
Stop Notes Do Worksheet
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