8.1 degree, standard form revised2 ink.notebook
Front cover
with choice
glued on top
January 05, 2017
back cover with
bell schedule
(if you want it)
Fold
very last
page in
INSIDE
Back
cover
need rubberband
and bookmark
Glue it to
the previous
page to make
your pocket
1
8.1 degree, standard form revised2 ink.notebook
On the Front
side of the very
last page (front
of your pocket)
Multiplication
Table
First page of
ISN
Glue your
envelope in.
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keep you
calculator
card here
January 05, 2017
INSIDE
Front
cover
First Formula
sheet with
Exponent
Rules on the
top
Other side
of the
envelope
Second
Formula sheet
with Solve
Factors on
the top
2
8.1 degree, standard form revised2 ink.notebook
Front of
second sheet
of paper
Table of Contents
page 1
8.1 degree and
standard form
of polynomials
January 05, 2017
On the BACK of the
THIRD sheet of
paper
glue and tape
your unit 8 tab
to the top
Page 1 - at the
top and at the
bottom
Unit 8 Polynomials
8.1 Degree and
Standard Form
Page 3
Page 2
3
8.1 degree, standard form revised2 ink.notebook
Lesson Objectives
Standards
Lesson Notes
Lesson Objectives
Standards
Lesson Notes
A.SSE.1 I will find the degree of a polynomial A.SSE.1 I will identify the leading coefficient of a polynomial A.SSE.2 I will rewrite a polynomial into standard form 8.1 Polynomials
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Lesson Objectives
January 05, 2017
Standards
Lesson Notes
A.SSE.1 Interpret expressions that represent a quantity in terms of its context.
EXCEPTIONS:
An expression that
No division by a variable
can have constants,
variables, and exponents Only whole number exponents
Named by degree and
Can't have an infinite
number of terms
number of terms
Polynomial
Example:
a) Interpret parts of an expression, such as terms, factors, and coefficients.
Characteristics:
My Definition:
4
5x6 + 4x2 - 1
5xy2 - 3x + 5y3 - 3
Counterexample:
x + y = 5 has equal sign
x + y-2 has negative exponent
2
x
has a variable on bottom
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4
8.1 degree, standard form revised2 ink.notebook
January 05, 2017
Polynomials can be named by the
number of terms
Terms
Name
Example
Let's Practice.
Name the following polynomials.
2. 2x2 ­ 3x4 + 5x + 6
1. –7 + 3n3
polynomial
binomial
4. 2x + 3y
3. 5
monomial
binomial
2
3
2
6. 2x + 5x + 6
5. 5x + 4x - x + 1
trinomial
polynomial
7. -x4 + 3x2 - 11
trinomial
8. 2x3y4
monomial
9.
10. 6x2 + 3y–1
monomial
binomial
trinomial
polynomial
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8.1 degree, standard form revised2 ink.notebook
January 05, 2017
Degree of a polynomial. The highest exponent or the sum of the exponents in a monomial.
11. 2x3y4 ­ monomial ­ add the exponents
12.2x4 + 3y8 ­ NOT a monomial ­ take the highest exponent
13. 2x2 + 5x2y3 + 6xy5 ­ add the exponents in each individual monomial and then find the highest
14.5x
15. 2
Find the degree of each polynomial. 16. 4x2y3z
17. –2abc
18. x4 − 6x2 − 2x3 − 10
19. 18x2 + 4yz − 10y
20. 22
21. 15m
22. − 2r8x4 + 7r2x − 4r7x6
23. 2x3y2 − 4xy3
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8.1 degree, standard form revised2 ink.notebook
January 05, 2017
Standard Form The terms of a polynomial are arranged so that the terms are in order from greatest degree to least degree. Leading Coefficient The number in front of the first term when the polynomial is in standard form.
Example:
-x5 + 8x4 - x2 - 15
(highest exponent is the first term)
Leading Coefficient: -1
Write each polynomial in standard form. Identify the leading coefficient.
24. 5x + 6 + 2x
2
25. − x2 − 2 + 5x4 + 3x
26. 5x + x2 + 6
27. 6x + 9 − 4x2
28. x4 + x3 + x2
29. 2x3 − x + 3x7
On the Worksheet
On Your
Whiteboards
7
8.1 degree, standard form revised2 ink.notebook
Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial, or trinomial. Then find the degree of the polynomial. Expression 1.
Monomial, Degree of Polynomial
the Binomial,or ? Trinomial? Polynomial January 05, 2017
Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial, binomial, or trinomial. 36
a)
b)
3x ­ 7xyz 2.
­25 3.
7n3 + 3n ­4 4.
9x3 + 4x + x + 4 + 2x 1 piece
Monomial
Monomial
Binomial polynomial
Binomial Trinomial
Trinomial
polynomial
Degree : 2 pieces
3 pieces
7x − x + 5
c)
d)
8g2h − 7gh + 2
Find the degree of each polynomial. (The highest exponent or the sum of the exponents in a monomial.)
9x2 + yz8
e)
Monomial
Binomial Trinomial
f) 8b + bc5
Monomial
polynomial
Binomial Trinomial
polynomial
g) h3m + 6h4m2 − 7 8
8.1 degree, standard form revised2 ink.notebook
Write each polynomial in standard form. Identify the leading coefficient.
h) 4 + 4x3 − 7x5 + 1
x
7 − x8
2x
j)
January 05, 2017
6 − x5 + 2x8
­3x
i)
k) 3x + 5x4 − 2 − x2
On the
Worksheet
To complete each sentence, write a letter from the column at the right.
_____1. 7 – 3x2 is a(n) __?__.
_____2. The degree of the polynomial 6x2 – 2x + 1 is __?__.
Homework
_____3. In 7x3 – 2x – 1, ­1 is a(n) __?__.
_____4. In 4x2 – 3x + 1, 2 is a(n) __?__.
_____5. The degree of the monomial ­1 is __?__.
a. monomial
b. binomial
c. trinomial
d. 0
e. 1
f. 2
g. 3
h. constant
i. exponent
j. variable
k. degree
_____6. 9y2 – 2y + 3 is a(n) __?__.
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8.1 degree, standard form revised2 ink.notebook
To complete each sentence, write a letter from the column at the right.
_____7. In the polynomial 3c3 – 2c + 1, c is the only __?__.
_____8. – 7x3y4 is a(n) __?__.
_____9. The degree of the polynomial 7 – 4x is __?__.
_____10. The __?__ of a monomial is the sum of the exponents of all of its variables.
a. monomial
b. binomial
c. trinomial
d. 0
e. 1
f. 2
g. 3
h. constant
i. exponent
j. variable
k. degree
January 05, 2017
Determine whether each expression is a
polynomial. If so, identify the polynomial
as a monomial, binomial, or trinomial.
12. 7ab + 6b2 – 2a3
15. 5m2p3 + 6
_____11. The degree of the polynomial 7x3 + 2x2 – 7x is __?__.
Determine whether each expression is a
polynomial. If so, identify the polynomial
as a monomial, binomial, or trinomial.
16. 2y – 5 + 3y2
13. 3x2
Find the degree of each polynomial.
18. −3
19. 6p3 – p4
20. −7z
21. 4h2j3 – h3k3
17. 5q−4 + 6q
10
8.1 degree, standard form revised2 ink.notebook
Find the degree of each polynomial.
22. 2a2b5 + 5 – ab 24. 3.5
23. 12 – 7q2t + 8r
25. 6df3 + 3d2f2
January 05, 2017
Find the degree of each polynomial.
26. 4x2 − 1
27. 4x4y − 8zx2 + 2x5
28. 9abc + bc − n5
29. 5x4 − 12x − 3x6
Write each polynomial in standard form. Identify the leading coefficient. Write each polynomial in standard form. Identify the leading coefficient. 30. −4x2 + 9x4 − 2x
32. 20x − 10x2 + 5x3
34. 2x5 – 12 + 3x
35. –y3 + 3y – 3y2 + 2
36. 4z – 2z2 – 5z4
37. 2a + 4a3 – 5a2 – 1 31. 2x + x2 − 5
33. x3 + x5 − x2
11
8.1 degree, standard form revised2 ink.notebook
Write each polynomial in standard form. Identify the leading coefficient. 38. 11t + 2t2 – 3 + t5
39. 2 + r – r3
43. Create a trinomial with a degree of 2, whose leading coefficient is –8
January 05, 2017
42. You have a coupon from The Really Quick Lube Shop for an $8 off oil change this month. An oil change costs $19.95, and a new oil filter costs $4.95. You use the coupon for an oil change and filter. Before adding tax, how much should you pay?
a) $11.95
b) $16.90
c) $24.90
d) $27.95
44. The Coaster Company started in 2005 with 40 employees. Since then it had grown at a steady rate of 10 employees per year. Write a linear equation that models the number of employees.
45. Ned rode 20 miles last week and plans to ride 35 miles per week. Write a linear equation that models the number of miles.
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8.1 degree, standard form revised2 ink.notebook
46. Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased tickets for $52.75.
Write a linear equation that models the number of adult tickets and student tickets.
January 05, 2017
Answers:
1) B 3) H 5) D 7) J 9) E 11) G 13) monomial 15) binomial 17) not a poly 19) 4 21) 6 23) 3 25) 4 27) 5 29) 6 31) x2 + 2x – 5, LC = 1 33) x5 + x3 – x2, LC = 1 35) –y3 – 2y2 + 3y + 2, LC = –1 37) 4a3 – 5a2 + 2a – 1, LC = 4
39) –r3 + r + 2, LC = –1 41) –b6 – 9b2 + 10b, LC = –1 43) WILL VARY: –8x2 + 2x+ 1
45) T = 20 + 35m 13