POLYNOMIALS.pptxxxxxxxxxxxxxxxxxxxxxxxxxxx

Polynomials

1. THE LANGUAGE OF ALGEBRA Evaluation of algebraic expressions Addition of polynomials Subtraction of polynomials Multiplication of polynomials Division of polynomials

2. OBJECTIVES: Evaluate algebraic expressions for given values of the variables; M7ALIIc-4 Recall the rules in operations on integers, the pemdas ; Add and subtracts polynomials; M7ALIId-2 and Perform operations on polynomials.

3. LESSON 1 Evaluation of algebraic expression

4. Rearrange the scrambled letters to form a word. HINT:  1. OMINBIAL = ___________ It is a polynomial with two terms.   2. RIAVABSLE = ___________ A symbol, usually denoted by a letter of the English alphabet which can represent one or more values.   3. SNOISSPREEX = ___________ An algebraic expression of a group of terms separated by plus or minus sign.   4. OMIALSLYNOP = ___________ It is a kind of algebraic expression where each term is a constant, a variable or a product of a constant and a variable.   5. ALMINOIRT = ___________ A polynomial with three terms.

5. An algebraic expression becomes more concrete when the value or number it represents is determined. The value of an algebraic expression is obtained when the variable is replaced by a real number. To substitute an algebraic expression is to substitute the given number to the variable and find the value of that expression. In evaluating algebraic expressions involving grouping symbols and exponents, you need to use the order of operations.

6. PEMDAS P – Perform all operations inside the Parentheses (P) or any grouping symbols. E – Evaluate expressions with Exponents (E). M – Perform Multiplication (M) and D – Division (D) from left to right A – Perform Addition (A) and S – Subtraction (S) from left to right.

7. Example 1: Evaluate when x = 2. Solution: → 1. Substitute 2 for the value of x in the expression → 2. Perform operation inside the P arentheses →3. Evaluate expressions with E xponents 2(25) - 4 → 4. Perform M ultiplication 50 - 4 → 5. Perform S ubtraction 46  

8. Example 2: Evaluate when x = - 2. Solution: → 1. Substitute - 2 for the value of x in the expression → 2. Evaluate expressions with E xponents → 3. Perform M ultiplication 8 + 6 +1 → 4. Perform A ddition 15  

9. Example 3: Evaluate each algebraic expression when a = 3 and b = 4. (a) (b) (c)  

10. PRACTICE: 1 DIRECTION : Choose the letter of the correct answer and write it on the space provided before each number. _____ 1. Evaluate when m = -3 a. 21 b. 22 c. 23 d. 24 _____ 2. Evaluate when x = 2 a. 18 b. 19 c. 16 d. 17 _____ 3. Evaluate when y = -2 a. 11 b. 12 c. 13 d. 14 _____ 4. Evaluate when a = 4 a. 23 b. 43 c. 13 d. 33 _____ 5. Evaluate when s = 3 a. 10 b. 20 c. 30 d. 40  

11. LESSON 2 Addition Polynomials

12. Simplifying algebraic expressions requires a skill in identifying similar terms. Similar terms can be combined by adding or subtracting their numerical coefficients. This is justified by the distributive property of multiplication over addition

13. ADDITION OF POLYNOMIALS METHOD 1 (Adding polynomials vertically) 1. Line up in similar terms. 2. Add the numerical Coefficients. 3. Retain the literal coefficients. METHOD 2 (Adding polynomials horizontally) 1. Group the similar terms. 2. Add the numerical Coefficients. 3. Retain the literal coefficients.

14. Example 1: Add the polynomials and Solution: METHOD 1 METHOD 2 ( )  

15. Example 2: Add 3 - 8 +2x-10 and 3 -6 +10x+8 Solution: METHOD 1  

16. Example 2: Add 3 - 8 +2x-10 and 3 -6 +10x+8 Solution: METHOD 2  

17. Example 3: Find the sum of and Solution: (METHOD 1)  

18. Example 3: Find the sum of and Solution: (METHOD 2) )  

19. ADDITION OF POLYNOMIALS and and 5 - 7 +3x – 8 and 3 - 4 + 2x - 7 -3 4 + x and -4 - 7 +4x – 9 and - 5  

20. LESSON 3 Subtraction Polynomials

21. Subtraction is the process of adding the additive inverse that is Hence to subtract a polynomial, write the subtraction statement to its equivalent addition statement by changing the subtrahend to its additive inverse.  

22. SUBTRACTION OF POLYNOMIALS METHOD 1 (Subtracting polynomials vertically 1. Change the sign of each term in the subtrahend. 2. Line up in similar terms. 2. Add the numerical Coefficients. 3. Retain the literal coefficients.

23. SUBTRACTION OF POLYNOMIALS METHOD 2 (Subtracting polynomials horizontally) 1. Change the sign of each term in the subtrahend. 2. Group the similar terms. 3. Add the numerical Coefficients. 4. Retain the literal coefficients.

24. Example 1: Find the difference between and Solution: - + -  

25. Example 1: Subtract the polynomials and Solution: - +  

26. PRACTICE: 3 DIRECTION : Subtract the following polynomials. and and and and and  

27. LESSON 4 Multiplication Polynomials

28. To multiply a monomial and a polynomial, use the distributive property to multiply the monomial with each term of the polynomial. RULES in MULTIPLYING POLYNOMIALS: 1. To multiply a monomial by another monomial , simply multiply the numerical coefficients then multiply the literal coefficients by adding its exponents.

29. Examples:  

30. 2. To multiply a monomial by a polynomial , simply apply the distributive property and follow the rule in multiplying a monomial by a monomial. Example: a. b.  

31. 3. To multiply a binomial by another binomial , simply distibute the first term of the first binomial to each term of the other binomial then distribute the second term to each term of the other binomial and simplify the results bu combining similar terms. This procedure is also known as the F – O – I – L method.

32. Example 1: a. Solution: F → O → I → L →  

33. b. Solution: F → O → I → L →  

34. Solution: F → O → I → L →  

35. PRACTICE: 2 DIRECTION : Solve the following. (r – 7) 2  

36. LESSON 5 Division of Polynomials

37. Recall addition of similar fractions. a The process can be reversed as shown below.  

38. Rule in Dividing Polynomials To divide a polynomial by a monomial, simply divide the numerical coefficients then divide the literal coefficients by subtracting its exponents. Example 1: Divide Solution:  

39. Example 2: Divide Solution:  

40. Example 3: Find the quotient of Solution:  

41. PRACTICE: 5 DIRECTION : Solve the following. 1. 4. . 2. 5. 3.