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6.3 pgs. 495-498 EQ: How can you classify and evaluation polynomials? Date: Questions/Main Points

A monomial in x is a term of the form: 𝑘𝑥𝑛 where k is ________________________________

and n is a _________________________. n is called the ____________________ of the term,

and k is called the _____________________.

A monomial may have more than one variable, and the degree of such a monomial is the

________________________________ of its variables:

For example: 4𝑥2𝑦3 is a ________________ monomial in x and y.

Monomials DO NOT have fractional or negative exponents.

Classify the following: 3√𝑥 17 3𝑥 −15𝑥23 2

7𝑎4 𝜋𝑥2 4𝑎−2 √2𝑥3

Monomials Not Monomials

A ____________________ is a monomial or the indicated sum or difference of monomials. The

_____________ of a polynomial is the ____________________ of the degrees of its terms. The

coefficient of the term of the largest degree is called the _______________________________.

Monomial Polynomial with 1 term

Binomial Polynomial with 2 terms

Trinomial Polynomial with 3 terms

1) 3𝑥4 2) 5𝑦2 − 2𝑦 + 1 3) −2𝑥−2 4) 8𝑥3 − 7

5) 14𝑎7 − 2𝑎 − 6 6) 17𝑥23 7) 6𝑎3 + 5𝑎2 − 𝑎−3 8) −3𝑦4 + 2𝑦2 − 9

9) 1

2𝑥3 − 2

5𝑥 10) 5

8𝑥5 + 2

3𝑥4

Monomial:

Polynomial:

Identify the expression as a monomial, binomial, trinomial or not a polynomial:

316

areal numberwhole number degreecoefficient

sumof thedegrees5th

170

17 3X 3a text 3A ya 215213

z 3

polynomialdegree largest

leadingcoefficient

2 2 or 4as or 183 5 or att 32 6 7 or 9a38aZ 12A

Monomial Trinomial Nota Binomial4thdegree 2nddegree polynomialcant 3rddegree

havenegative

fexponents

Trinomial Nota Nota 9 Trinomial7thdegree polynomial polynomial 4thdegreeFractionalexponent

Binomial Binomial3rddegree 5thdegree

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6.3 pgs. 495-498 EQ: How can you classify and evaluation polynomials? Date: Questions/Main Points

Simplify each of the following polynomials by combining like terms. Write the polynomial in descending order and state the degree and type of the polynomial. a) 5𝑥3 + 7𝑥3 b) 5𝑥3 + 7𝑥3 − 2𝑥 c) 1

2𝑦 + 3𝑦 − 2

3𝑦2 − 7

d) 𝑥2 + 8𝑥 − 15 − 𝑥2 e) −3𝑦4 + 2𝑦2 + 𝑦−1 Evaluate 𝑝(𝑥) = 4𝑥2 + 5𝑥 − 15 for 𝑥 = 3. Evaluate 𝑝(𝑦) = 5𝑦3 + 𝑦2 − 3𝑦 + 8 for 𝑥 = −2.

Summary:

Simplifying Polynomials:

Evaluating Polynomials:

3 6

51 7 3 12 3 3rddegreemonomial

5 7 3 2x 12 3 2x 3rddegreebinomial

2342 3112 y 72342 124 7 2nddegree trinomial

8 15 1st degreebinomial

Nota polynomialduetonegativeexponent

functionNotation

samfasP33 4135 513 15

419 t 15 1536

pts 36

y

plz 5143 25312 8518 4 6 840 4 6 873 6 8

s30 8

pl2 22

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HW: 6.3 pgs., 499-501

Answer Column

12) ______________________

______________________

19) ______________________

______________________

20) ______________________

______________________

21) ______________________

______________________

26) ______________________

______________________

27) ______________________

______________________

Simplify the polynomial. 1) Write the polynomial in descending order 2) Then state the degree and type of the simplified polynomial

12) 4𝑥2 − 𝑥 + 𝑥2 19) 6𝑎5 + 2𝑎2 − 7𝑎3 − 3𝑎2

20) 2𝑥2 − 3𝑥2 + 2 − 4𝑥2 − 2 + 5𝑥2

21) 4𝑦 − 8𝑦2 + 2𝑦3 + 8𝑦

26) −3𝑦5 + 7𝑦 − 2𝑦3 − 5 + 4𝑦2 + 𝑦2 27) 𝑥4 + 3𝑥4 − 2𝑥 + 5𝑥 − 10 − 𝑥2 + 𝑥

5 2 x2nddegreebinomial

µ ix2 x5 2 x

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HW: 6.3 pgs., 499-501

Answer Column

31) ____________

32) ____________

35) ____________

36) ____________

Evaluate the given polynomials as indicated. 31) Given 𝑝(𝑥) = 𝑥2 + 14𝑥 − 3 find 𝑝(−1).

32) Given 𝑝(𝑦) = 𝑦3 − 5𝑦2 + 6𝑦 + 2 find 𝑝(2).

35) Given 𝑝(𝑥) = 8𝑥4 + 2𝑥3 − 6𝑥2 − 7 find 𝑝(−2).

36) Given 𝑝(𝑎) = 𝑎3 + 4𝑎2 + 𝑎 + 2 find 𝑝(−5).

plD 16

ptt L15144ft 31 14 3IB 316