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21 | P a g e
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: đđ„đ 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: 4đ„2đŠ3 is a ________________ monomial in x and y.
Monomials DO NOT have fractional or negative exponents.
Classify the following: 3âđ„ 17 3đ„ â15đ„23 2
7đ4 đđ„2 4đâ2 â2đ„3
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) 3đ„4 2) 5đŠ2 â 2đŠ + 1 3) â2đ„â2 4) 8đ„3 â 7
5) 14đ7 â 2đ â 6 6) 17đ„23 7) 6đ3 + 5đ2 â đâ3 8) â3đŠ4 + 2đŠ2 â 9
9) 1
2đ„3 â 2
5đ„ 10) 5
8đ„5 + 2
3đ„4
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
23 | P a g e
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) 5đ„3 + 7đ„3 b) 5đ„3 + 7đ„3 â 2đ„ c) 1
2đŠ + 3đŠ â 2
3đŠ2 â 7
d) đ„2 + 8đ„ â 15 â đ„2 e) â3đŠ4 + 2đŠ2 + đŠâ1 Evaluate đ(đ„) = 4đ„2 + 5đ„ â 15 for đ„ = 3. Evaluate đ(đŠ) = 5đŠ3 + đŠ2 â 3đŠ + 8 for đ„ = â2.
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
20 | P a g e
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) 4đ„2 â đ„ + đ„2 19) 6đ5 + 2đ2 â 7đ3 â 3đ2
20) 2đ„2 â 3đ„2 + 2 â 4đ„2 â 2 + 5đ„2
21) 4đŠ â 8đŠ2 + 2đŠ3 + 8đŠ
26) â3đŠ5 + 7đŠ â 2đŠ3 â 5 + 4đŠ2 + đŠ2 27) đ„4 + 3đ„4 â 2đ„ + 5đ„ â 10 â đ„2 + đ„
5 2 x2nddegreebinomial
” ix2 x5 2 x
22 | P a g e
HW: 6.3 pgs., 499-501
Answer Column
31) ____________
32) ____________
35) ____________
36) ____________
Evaluate the given polynomials as indicated. 31) Given đ(đ„) = đ„2 + 14đ„ â 3 find đ(â1).
32) Given đ(đŠ) = đŠ3 â 5đŠ2 + 6đŠ + 2 find đ(2).
35) Given đ(đ„) = 8đ„4 + 2đ„3 â 6đ„2 â 7 find đ(â2).
36) Given đ(đ) = đ3 + 4đ2 + đ + 2 find đ(â5).
plD 16
ptt L15144ft 31 14 3IB 316