Real problems in science or in business occur in ordinary language. To do such problems, we typically have to translate them into algebraic language. Problem 7. Write an that will symbolize each of the following. algebraic expression a) Six times a certain number. 6n, or 6x, or 6m. Any letter will do. b) Six more than a certain number. + 6 x c) Six less than a certain number. 6 x − d) A certain number less than 6. 6 x − e) A number repeated as a three times. = x· x· x x3 f) A number repeated as a term times. + + x x x g) The sum of three consecutive whole numbers. The for example, idea, g) of 6 + 7 + 8. [Hint: Let be the first number.] x g) + (x + 1) + (x + 2) x h) less than twice a certain number. 2x 8 − i) One more than three times a certain number. 3x + 1 Now an algebraic is not a sentence, it does not have a verb, which is typically the expression equal sign =. An algebraic has an equal sign. statement FACTORIZATION OF ALGEBRAIC EXPRESSIONS In the previous section we expanded expressions such as to giveThe reverse of this process is called factorizing. To factorize linear expressions: We can check the answer by multiplying out the brackets: 2(2x+3) = 4x+6 Example Factorise 4x² + 6x. In this case 2x is the highest factor of both 4x² and 6x, so 2x will go outside the brackets. The remaining factors of each term are left inside the brackets, where they are recombined. We can the answer by multiplying out the brackets: 2x(2x+3) = 4x²+6x
Real problems in science or in business occur in ordinary language. To do such problems, we typically have to translate them into algebraic language. Problem 7. Write an algebraic expression that will symbolize each of the following. a) Six times a certain number. 6n, or 6x, or 6m. Any letter will do. b) Six more than a certain number. x + 6 c) Six less than a certain number. x − 6 d) A certain number less than 6. 6 − x e) A number repeated as a three times. x· x· x = x3 f) A number repeated as a term times. x + x + x g) The sum of three consecutive whole numbers. The idea, for example, g) of 6 + 7 + 8. [Hint: Let x be the first number.] g) x + (x + 1) + (x + 2) h) less than twice a certain number. 2x − 8 i) One more than three times a certain number. 3x + 1 Now an algebraic expression is not a sentence, it does not have a verb, which is typically the equal sign =. An algebraic statement has an equal sign. FACTORIZATION OF ALGEBRAIC EXPRESSIONS In the previous section we expanded expressions such as to giveThe reverse of this process is called factorizing. To factorize linear expressions: We can check the answer by multiplying out the brackets: 2(2x+3) = 4x+6 Example Factorise 4x² + 6x. In this case 2x is the highest factor of both 4x² and 6x, so 2x will go outside the brackets. The remaining factors of each term are left inside the brackets, where they are recombined. We can the answer by multiplying out the brackets: 2x(2x+3) = 4x²+6x
BMS_411S_LECTURE_NOTES.docx