old math 1 polys.notebook
Intro to Polynomials
November 28, 2016
Standard form of a polynomial means that the degrees of its monomial terms decrease from left to right.
Definitions
1) Polynomial ­ a monomial or the sum of monomials (1,2,3 or more terms)
2) Binomial ­ the sum of two monomials (2 Terms)
The degree of a polynomial in one variable is the same as the degree of the monomial with the greatest exponent. Ex: The degree of 3x4 + 5x2 ­ 7x + 1 is 4.
3) Trinomial ­ the sum of three monomials (3 Terms)
Monomial
7
13n
Binomial
Trinomial
3 + 4y
x + y + z
p + 5p + 4
Polynomial
Degree
Name Using Degree
Number of Terms
Name Using Number of Terms
Monomial
6
0
Constant
1
5x + 9
1
Linear
2
Binomial
4x2 + 7x + 3
2
Quadratic
3
Trinomial
2x3
3
Cubic
1
Monomial
8x ­ 2x3 + 3x
4
Fourth degree
3
Trinomial
2
2a + 3c
­5z3 6x2 + 3y
2
2 a ­ 2ab ­ b
4
3 2
2
4ab c 7pqr + pq 2 3v ­ 2w + ab+6
Oct 19­1:02 PM
Nov 17­11:22 PM
Ex.1) State whether each expression is a polynomial. If it is, identify it as a monomial, binomial, or trinomial and state the degree name as well.
Law of Exponents Review:
1. ( −3 )
2. (4 ) 2
a) 2x ­ 3yz
2 2
8 5
3. −3 15 c) ­8
0 8
d) 4a 2 + 5a + a + 9
4. ( 4 2)3
4
(2 ) 4) degree of a polynomial ­ greatest exponent ( add the exponents in each monomial in the polynomial, the monomial with the greatest sum indicates the degree )
5. (3 ) 2 −3
b) 8n3 + 5n ­2
2 Ex.2) Find the degree of each polynomial.
6. ( 10 )(−2 5) a) 5mn2
b) ­4x2 y2 + 3x 2 + 5
c) 3a + 7ab ­ 2a 2 b + 16
d) 12 + 5b + 6bc + 16
e) 9x 2 ­ 2x ­4
f) 14g2 h5 i
Nov 21­7:38 AM
Ex.3) Arrange in Standard Form (decending order for x).
Oct 19­1:25 PM
Adding and Subtracting Polynomials
*To add or subtract polynomials, you combine like terms.
a) 16 + 14x3 + 2x ­ x2
Ex.1) Simplify.
b) 7 + 4x + 2x ­ x
a) ( 3x 2 ­ 4x + 8 ) + ( 2x ­ 7x 2 ­ 5)
c) 8 + 7x2 ­ 12x3 ­ 4x
b) ( 3n2 + 13n 3 + 5n) ­ ( 7n + 4n 3 )
3
2
d) a4 + ax2 ­ 2axy3 ­ 9x4 y
c) ( 7y 2 + 2y ­3 ) + ( 2 ­ 4y + 5y 2 )
d) ( 11 + 4d 2 ) ­ ( 3 ­ 6d 2 )
e) ( x 3 ­ 7x + 4x 2 ­ 2 ) ­ ( 2x 2 ­9x + 4)
Oct 19­3:48 PM
Oct 19­4:04 PM
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old math 1 polys.notebook
Ex.2) The measure of the perimeter of a triangle is 37s + 42.
a) Find the polynomial that represents the
14s + 16
third side of the triangle.
b) Find the length of the third side if s = 3.
10s + 20
November 28, 2016
Ex.4) Travel A researcher studied the number of overnight stays in U.S. National Park Service campgrounds and in the backcountry of the national park system over a 5­yr period. The researcher modeled the results in thousands, with the following polynomials.
Campgrounds: ­7.1x2 ­ 180x + 5800
Backcountry: 21x2 ­ 140x + 1900
x = 0 corresponds to the first year in the 5­yr period
What polynomial models the total number of overnight stays in both campgrounds and backcountry?
Ex.5) A nutritionist studied the U.S. consumption of carrots and celery and of broccoli over a 6­yr period. The nutritionist modeled the results, in millions of pounds, with the following polynomials. Carrots and celery: ­12x3 + 106x2 ­ 241x + 4477
Broccoli: 14x2 ­ 14x + 1545
x = 0 corresponds to the first year in the 6­yr period
What polynomial models the total number of pounds, in millions, of carrots,
celery, and broccoli consumed in the United States during the 6­year period?
Oct 20­10:27 AM
Nov 17­11:52 PM
Multiplying a Polynomial by a Monomial
*To multiply a polynomial and monomial, use the Distributive Property.
Homework: Page 459 # 2­38 even, 39­41 all, 49,50,55
Ex.1) Simplify.
a) ­2x 2 ( 3x2 ­ 7x + 10 )
b) 4( 3d 2 + 5d ) ­ d( d 2 ­ 7d + 12)
c) 6y( 4y 2 ­ 9y ­ 7)
d) 3( 2t 2 ­ 4t ­ 15) + 6t( 5t + 2)
Mar 30­9:34 AM
Ex.2) Solve.
a) y( y ­ 12) + y( y + 2) + 25 = 2y( y + 5) ­ 15
Oct 20­10:42 AM
Ex.3 Admission to the State Fair is $10. Once in the fair, super rides are an additional $3 each and regular rides are $2 each. Brittany goes to the fair and rides 15 rides, of which s of those are super rides.
a) Find an expression for how much money Brittany spent at the
fair.
b) Evaluate the expression to find the cost if Brittany rode 9 super
rides.
b) b( 12 + b) ­ 7 = 2b + b( ­4 + b)
c) 3g( g ­ 4) ­ 2g( g ­ 7) = g( g + 6) ­28
d) k( k ­ 7) + 10 = 2k + k(k + 6)
Oct 20­10:50 AM
Oct 20­10:55 AM
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old math 1 polys.notebook
November 28, 2016
Multiplying Polynomials
Obj.: TLW 1) multiply two binomials by using the FOIL method.
2) multiply two polynomials by using the distributive property.
3) multiply by using the Box method.
*FOIL Method: To multiply binomials, multiply
First terms
Outer terms
Inner terms
Last terms
Ex.1) Find each product by using FOIL or Box method.
b) ( x ­ 5)( x + 7)
c) (2y + 3)(6y ­ 7)
d) ( y + 8)( y ­ 4)
a) ( x + 3)( x + 2)
e) ( z ­ 6)( z ­ 12)
x + 3
f) ( 5x ­ 4)( 2x + 8)
x
+
2
Oct 20­11:00 AM
Ex.1) Find each product by distributing or using Box method.
Oct 20­11:10 AM
c) ( 3a + 4)( a2 ­ 12a + 1)
a) ( 4x + 9)(2x2 ­ 5x + 3)
b) (y2 ­ 2y + 5)(6y2 ­ 3y + 1)
c) ( 3a + 4)( a2 ­ 12a + 1)
d) (2b2 + 7b + 9)( b2 + 3b ­ 1)
d) (2b2 + 7b + 9)( b2 + 3b ­ 1)
Oct 20­11:13 AM
Homework:
Page 463 # 2­12 even
Page 469 # 6­20 even, 21,42,43,45
Oct 20­11:16 AM
Warm Up:
1. (x + 3)(x + 7)
2. (2x ‐ 3)(x + 10)
3. 3xy3(5x2y + 2x)
4. (x2 ‐ 5)(5x2 + 2x)
5. (x2 + 4x ‐ 5) ‐ (4x2 ‐ 8x)
Nov 22­6:55 AM
Nov 28­6:58 AM
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old math 1 polys.notebook
November 28, 2016
Warm Up: The blue rectangle has a yellow rectangle cut out of it. Lengths of the rectangles are given in the form of binomials. Find the area of the remaining blue rectangle. Your answer will be in the form of a polynomial.
Special Products
Obj.: TLW 1) find the squares of sums and differences.
2) find the product of a sum and difference.
x + 4
x+2
Square of a Sum: ( a + b )2 = ( a + b )( a + b ) = a2 + 2ab + b2
Square of a Difference: ( a ­ b)2 = ( a ­ b )( a ­ b) = a2 ­ 2ab + b2 x ­ 1
Product of a Sum and a Difference: ( a + b)( a ­ b) = a2 ­ b2
x + 10
Ex.) Find each product.
1) ( 4y + 5)2
Nov 22­6:57 AM
Oct 21­12:48 PM
5) ( 7z + 2)2
2) ( 8c + 3d)2
6) ( 5q + 9r )2
3) ( 6p ­ 1)
2
7) ( 3c ­ 4 )2
4) ( 5m3 ­ 2n)2
Oct 22­11:26 AM
Oct 22­11:27 AM
8) ( 6e ­ 6f)2
11) ( 9d ­ 4)( 9d + 4)
9) ( 3n + 2) ( 3n ­ 2)
12) ( 10g + 13h3 )( 10g ­ 13h3 )
10) ( 11v ­ 8w2 )(11v + 8w2 )
Oct 22­11:28 AM
Oct 22­11:31 AM
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old math 1 polys.notebook
November 28, 2016
Homework:
Pg 477 # 2­8e, 16­20e, 26,27,44­52 even
Apr 2­8:58 PM
Apr 2­8:53 PM
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