2. What does the word “distribute” mean? Give two examples of the word in everyday use. 3. In math, distribute means to multiply out the parts of an e...
Lesson 8: Adding and Subtracting Polynomials Exploratory Exercise Kim was working on a problem in math when she ran across this problem. Distribute and simplify if possible. 2(3x + 5) Kim’s dad said, “I remember doing something like this in school.” He then drew two arcs on her paper. Distribute and simplify if possible. 2(3x + 5)
1. Talk to your partner about what Kim’s dad was trying to show. Then complete Kim’s problem.
In Lesson 7, you mainly used the commutative and associative properties, and only looked at examples of the distributive property. In this lesson we’ll look closer at the distributive property and then in the next lesson you’ll extend your knowledge about this important property. 2. What does the word “distribute” mean? Give two examples of the word in everyday use.
Distribute in real-life means to hand out. For example: He distributed the blankets to all the campers. I distributed the food samples at the store.
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3. In math, distribute means to multiply out the parts of an expression. How does this definition relate to your definition from Exercise 2?
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Lesson 8
Hart Interactive – Algebra 1
M1
ALGEBRA I
ADDING POLYNOMIALS 7. Add the following polynomials by combining like terms. Be careful – you will have to distribute in a few of them. A.
(3 x + 5) + (7 x − 3)
B.
(2 x 2 − 3) + (7 x + 2)
C.
(3 x + 4) + (−4 x − 7)
D.
(4 x − 5) + 2(3 x + 1)
E.
−2(4 x 2 + 6) + (7 x 2 − 9 x + 3)
F.
− x(4 x3 − 5 x + 6) + (6 x 2 + 7 x − 3)
SUBTRACTING POLYNOMIALS When subtracting polynomials, you will need to distribute the negative sign to all the terms in the parentheses. 8. Subtract these polynomials and then combine like terms. A.
S.69 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 8
Hart Interactive – Algebra 1
M1
ALGEBRA I
9. Determine which word matches each definition. Word Bank Polynomial
Monomial
Binomial
Trinomial
Degree of a Term
Degree of a Polynomial
Standard Form of a Polynomial
Definition A. The sum of the exponents of the variable symbols that appear in the monomial B. A polynomial with only two terms C. The sum (or difference) of monomials D. The degree of the monomial term with the highest degree
Word
Degree of a term
Binomial
Polynomial
F. An algebraic expression generated using only the multiplication operator (×). Thus, it does not contain + or − operators.
Degree of polynomial
Standard form of a polynomial
Monomial
G. A polynomial with only three terms
Trinomial
E. The terms are rewritten so that the terms are in order from greatest degree to least degree
10. Go back to Exercises 7 and 8 and write each polynomial in standard form, if it isn’t already in standard form, and then determine the degree of the resulting polynomial. 11. Janie writes a polynomial expression using only one variable, 𝑥𝑥, with degree 3. Max writes a polynomial expression using only one variable, 𝑥𝑥, with degree 7. A. What can you determine about the degree of the sum of Janie’s and Max’s polynomials?
It must have a degree of 7. B. What can you determine about the degree of the difference of Janie’s and Max’s polynomials?
