2. In the product of two or more numbers, any one of them or the product of any number of them is a factor of the given product. 2.3.5 = 30. Then, 2 is a factor of 30. 2.3 or 6 is also a factor of 30. 3. A term is a number whose parts are not separated by the plus (+) or minus (—) sign. In the expression, 10+6 10 is a term. 6 is also a term. 10+6 is composed of two terms. 4. A binomial is an expression of two terms. An expression of two or more terms is also called a polynomial. 100+60 + 3 is a trinomial. 5. It is often necessary to represent a number by a letter or a combination of letters. Such letters may represent either unknown numbers or those supposed to be known numbers. This kind of notation is used in general arithmetic or algebra. E.g., n may represent any number, likewise any letter or combination of letters and figures may be considered a number. a+b+c is a trinomial number (§ 4), or the sum of three numbers a, b, and c. In arithmetic it is possible to express such a sum as a single number. Thus, 2+5+ 8 = 15. In algebra, this is not possible unless the terms of the expression are alike or similar. 6. Similar Terms are terms which differ in their coefficients only, e.g., 5, 6. x, ax, b. x. 7. Any factor (§ 2) of a number is the coefficient of the remaining factors. Thus, in a x, a is the coefficient of x. in 2. 3, 2 is the coefficient of 3. in 2. 3, 3 is the coefficient of 2. in 2 a. b, 2 in 2 in 2 b is the coefficient of a. ab, a is the coefficient of 2. b. a. b, 2 is the numerical coefficient of a ⚫ .b. in ax, a is the literal coefficient of x. When the product of a number of figures and letters is to be written, the multiplication sign is usually omitted. 8. 2a+3a +7 a is a trinomial consisting of similar terms. (§ 6). These terms may be united into one term by finding the sum of the coefficients. Hence, 2a+3a+7a= (2+3+7) a = 12 a. This is the same operation as that in arithmetic when one finds the value of and is brought still closer to arithmetic when one remembers that only like numbers can be added. means that 3 ab is to be subtracted from 15 ab, and 7 ab added to this difference. Ex. 1. Find the sum of 20 xy + 4 xy-7 d. 20 xy+4 xy-7 d= (20 xy + 4 xy)-7 d= 24 xy-7 d. Ex. 2. Add 5 a2 + 3 ab +4 b2 and 4 a2 - 2 ab - 4 b2. |