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Arithmetic with Polynomials & Rational Expressions Name: ____TEACHER COPY ______ _______ CCSS.Math.Content.HSA.APR.A.1 Date: ______________________ Period: _____ Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Lesson Plan: 1. Hook (source: jokes4us.com): Surgeon: Nurse! I have so many patients! Who do I work on first? Nurse: Simple. Use the order of operations 2. Introduction and Vocabulary: In order to understand and simplify polynomial expressions, we need to first discuss some vocabulary used with them: commutative, associative, identity, distributive properties, monomial, binomial, trinomial, terms, like terms, degree, coefficients. 3. Guided Practice: After the properties review, help students compare different terms and note the degree and reasoning for each. SUe the properties to simplify polynomial expressions. Show them the standard way that polynomials are written in descending order. 4. Independent Practice : Students complete the problems through number 20 on their own (or with a partner). Review together and correct discrepancies. 5. Exit Slip: How can you tell what the degree of a polynomial is? Describe how to write a polynomial in descending order. Use your own example if you wish. Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. All Rights Reserved by NewMathTeacher.Net Arithmetic with Polynomials & Rational Expressions Name: ____________________ ______ _______ CCSS.Math.Content.HSA.APR.A.1 Date: ______________________ Period: _____ Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Review of Properties of Real Numbers Let a, b, and c be real numbers. Commutative Property of Addition Commutative Property of Multiplication a+b=b+a a•b=b•a Associative Property of Addition Associative Property of Multiplication (a + b) + c = a + (b + c) (a • b) • c = a • (b • c) Identity Property of Addition Identity Property of Multiplication a+0=0+a=a a•1=1•a=a Distributive Property a(b + c) = ab + ac a(b – c) = ab - ac (b + c)a = ba + ca (b – c)a = ba - ca Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. All Rights Reserved by NewMathTeacher.Net Classify the polynomial by the number of terms and state the degree of the polynomial. Polynomial Monomial, Trinomial, Binomial Degree 1. x4 – 3x2 - 7 2. -4x6y 3. -3y + 2 Write the polynomial so that the exponents are in descending order. HINT: For additional & subtraction, vertically line up the like terms. For multiplication, use the box method. ______________4. (3x2 + 2x - 5) + (7x2 – 3x + 2) ______________5. (x + 7) + (6x - 1) – (-5x + 3) ______________6. -3a2(a2 – 3a + 5) ______________7. (x + 7)(x - 4) ______________8. (3x + 2)(x + 5) ______________9. (t + w)(t – w) ______________10. (3x + 2)2 BONUS PROBLEM: (x + 2)(x – 3)(x + 1) Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. All Rights Reserved by NewMathTeacher.Net Zero Product Property & Factoring Polynomials Solve the equation for x. 11. (x - 7)(x + 3) = 0 12. (x - 5)(x + 4) = 0 13. (2x - 1)(3x + 8) = 0 Factor out the greatest common monomial factor. 14. 7x2 - 7x = ____ ( ) 15. 2m3 + 8m2 - 4m = ____ ( ) Now, combine the two skills you've learned above... Solve the equation by factoring. 16. 2x2 + 8x = 0 17. 6n2 = 15n 18. a2 + 5a = 0 19. 4x2 = 2x Solve a multi-step word problem. 20. A startled armadillo jumps straight into the air with an initial vertical velocity of 14 feet per second. After how many seconds does it land on the ground? Vertical motion model: h = –16t2 + vt + s where v is velocity and s is the initial height (zero) Substitute 0 for h. When the armadillo lands, its height above the ground is 0 feet. Solve for t. The armadillo lands on the ground _____ second after the armadillo jumps. Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. All Rights Reserved by NewMathTeacher.Net