Addition and Subtraction of Polynomials.pptx
- 1. Lesson 1 Addition and Subtraction of Polynomials
- 2. Objectives At the end of this lesson, the learner should be able to correctly identify the different classifications of polynomials according to degree and number of terms; accurately add and subtract polynomials; and correctly solve word problems involving addition and subtraction of polynomials.
- 3. Essential Questions How are polynomials classified? How do you add and subtract polynomials? How is addition and subtraction of polynomials related to one another?
- 4. Warm Up! Before we start our proper lesson, let us test your skills in adding and subtracting integers. (Click on the link to access the exercise.) “Add and Subtract Integers”. Math Games. Retrieved 8 May 2019 from https://www.mathgames.com/skill/7.65-add-and-subtract-integer s
- 5. Guide Questions ● How many questions did you answer correctly? ● What if there are integers which serves as numerical coefficients of terms? How do we perform these operations? ● Do you think you are ready to add and subtract polynomials?
- 6. Learn about It! Polynomials algebraic expressions with nonnegative integer powers and no variables in the denominator 1 Examples: a. c. e. b. d.
- 7. Learn about It! Term element of a polynomial, which is either a constant or a constant multiplied with a variable containing a nonnegative integer power 2 Example:
- 8. Learn about It! Like terms terms that differ only in their numerical coefficients; that is, they have the same variable and nonnegative exponent 3 Examples: a. and b. and
- 9. Learn about It! Monomial a polynomial that has one term 4 Examples: a. b. c.
- 10. Learn about It! Binomial a polynomial that has two terms 5 Examples: a. b. c.
- 11. Learn about It! Trinomial a polynomial that has three terms 6 Examples: a. b. c.
- 12. Learn about It! Degree of a polynomial highest sum of exponents of variables in a term 7 Examples: 8 has a degree of 0 has a degree of 1 has a degree of 2 (quadratic polynomial) has a degree of 3 (cubic polynomial) has a degree of 3 because has a degree of 3 ( has a degree of 2 and has a degree of 1, thus ) and has also a degree of 3.
- 13. Learn about It! Adding and Subtracting Polynomials this can be done by arranging the polynomials being added or subtracted in two separate rows and aligning the like terms 8 Examples: a. It is easier if the like terms are placed in same vertical column. (+)
- 14. Learn about It! b. For subtraction of polynomials, change the subtraction operation to addition, then change the signs of all the terms in the subtrahend. (-) (+)
- 15. Try It! Example 1: Add the following polynomials: and
- 16. Try It! Example 1: Add the following polynomials: and Solution: We can add the given polynomials in two ways: A. Horizontal method
- 17. Try It! Example 1: Add the following polynomials: and Solution: 1. Group like terms.
- 18. Try It! Example 1: Add the following polynomials: and Solution: 2. Add or simplify the like terms.
- 19. Try It! Example 1: Add the following polynomials: and Solution: B. The vertical method
- 20. Try It! Example 1: Add the following polynomials: and Solution: 1. Write the polynomials in two rows. Make sure that the like terms are aligned.
- 21. Try It! Example 1: Add the following polynomials: and Solution: 2. Add or simplify the like terms.
- 22. Try It! Example 1: Add the following polynomials: and Therefore, the sum of and is .
- 23. Try It! Example 2: Find the difference:
- 24. Try It! Example 2: Find the difference: Solution: Similar to Example 1, we can use the two methods. This time, we will use the vertical method.
- 25. Try It! Example 2: Find the difference: Solution: 1. Write the polynomials in two rows aligning like terms.
- 26. Try It! Example 2: Find the difference: Solution: 2. Change the subtraction operation to addition, then change the signs of all the terms in the subtrahend.
- 27. Try It! Example 2: Find the difference: Solution: 3. Add the polynomials.
- 28. Try It! Example 2: Find the difference: Therefore, the difference of and is .
- 29. Let’s Practice! Individual Practice: 1. Simplify the following: 2. What must be added to to get a sum of ?
- 30. Let’s Practice! Group Practice: To be done in groups of 4. The length of a picture frame is given by the expression units. If the width of the frame is expressed as units, how much longer is the length than the width?
- 31. Key Points Polynomials algebraic expressions with nonnegative integer powers and no variables in the denominator 1 3 Term element of a polynomial, which is either a constant or a constant multiplied with a variable containing a nonnegative integer power. Like terms are terms that differ only in their numerical coefficients; that is, they have the same variable and nonnegative exponent 2
- 32. Key Points Classification of Polynomials based on the number of terms; Monomial is a polynomial with one term. Binomial has two terms. Trinomial has three terms. 3 3 Degree of a polynomial highest sum of exponents of variables in a term 4 Adding and Subtracting Polynomials this can be done by arranging the polynomials being added or subtracted in two separate rows and aligning the like terms 5
- 33. Synthesis ● How do you add and subtract polynomials? ● Why is there a need to learn about addition and subtraction of polynomials? ● Now that you have learned about addition and subtraction of polynomials, can you apply your learning to multiplication and division of polynomials?