Martin-Gay, Beginning Algebra, 5ed 22 x x 3 2  x 5 2  x + 11 Polynomial Vocabulary Term – a number or a product of a number and variables raised to powers Coefficient – numerical factor of a term Constant – term which is only a number

Martin-Gay, Beginning Algebra, 5ed 33

44 In the polynomial 7x 5 + x 2 y 2 – 4xy + 7 There are 4 terms: 7x 5, x 2 y 2,  4xy and 7. The numerical coefficient of term 7x 5 is 7, of term x 2 y 2 is 1, of term –4xy is –4 and of term 7 is 7. 7 is a constant term.

Martin-Gay, Beginning Algebra, 5ed 55

= = 3 1  0 33 The degree of the polynomial is 5.

Martin-Gay, Beginning Algebra, 5ed 77 Like terms are terms that contain exactly the same variables raised to exactly the same powers. Combine like terms to simplify. (x 2 y + xy – y) + (10x 2 y – 2y + xy) Only like terms can be combined through addition and subtraction. Warning! = 11x 2 y + 2xy – 3y = (1 + 10)x 2 y + (1 + 1)xy + (– 1 – 2)y = x 2 y + 10x 2 y + xy + xy – y – 2y(Like terms are grouped together) Example:

Martin-Gay, Beginning Algebra, 5ed 88 Add 2(3x – 8) + 3(4x 2 – 3x +3) = 6x – x 2 – 9x + 9 = 12x 2 – 3x – 7 Example: 2(3x – 8) + 3(4x 2 – 3x +3) Subtract 4 – 5(– y – 4) Example: 4 –5 (– y – 4) = 4 + 5y + 20 = 5y + 24

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10 Example: = 14a 2 – 18a + 26  (– a 2 + 1) – 2(a 2 – 3) + 3(5a 2 – 6a + 7) = a 2 – 1 – 2a a 2 – 18a + 21 Simplify  (– a 2 + 1) – 2(a 2 – 3) + 3(5a 2 – 6a + 7)

Martin-Gay, Beginning Algebra, 5ed 11 Find the perimeter of the triangle. Example

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