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Transcript
```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
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.
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
Review of Properties of Real Numbers
Let a, b, and c be real numbers.
Commutative Property of Multiplication
a+b=b+a
a•b=b•a
Associative Property of Multiplication
(a + b) + c = a + (b + c)
(a • b) • c = a • (b • c)
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
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)
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.