Download CC Math I Standards: Unit 6 POLYNOMIALS: INTRODUCTION

CC Math I Standards: Unit 6
POLYNOMIALS: INTRODUCTION
MONOMIALS:
EXAMPLES:
 4 A number
y
A variable
NON-EXAMPLES:
Variable as an
2x
exponent
2
x  3 A sum
a2
The product of variables
5 a 2
3
x
1 2
The product of numbers
x y
and variables
2
Negative exponent
A quotient
Examples: Determine if each expression is a monomial.
2
1
x
1.  4 xy
2. a  8
4. 7 z
3.
5
7
5. b
POLYNOMIAL: A polynomial is a ________________ or the
_______________________________________ of different monomials.
6. 2q
Determine which expressions are polynomials:
a
c
ab

d

7.
8. p + q 9.
10. x2 + 4x – 8 11. 7y3 – 5y -2 + 4y
4
d
BINOMIAL:
SPECIFIC TYPES OF POLYNOMIALS
TRINOMIAL:
Examples:
Examples:
Examples #12 - 19: Determine if each expression is a monomial, binomial,
trinomial, or not a polynomial.
12. 2m  7
13. x 2  3 x  4  5
14.
5
3
2x
15. 3 y 2  6  7 y
16. 3x + 8x – 5x2
17. 8x3y2z
18. 2a2 + 3ab – 5ba
19. 9r + 11 – 5r2
CC Math I Standards: Unit 6
POLYNOMIALS: ADDITION AND SUBTRACTION
WARM UP ACTIVITY: Simplify the following
1) 3x – 2y + 4y – 6x
3) 4z + 2t + 3z – t
2) 3x – 12y – 2x2 + 6y
5) 8a + 6b + 6a + 2b
4) 5a + 3b – 2c – 8a
ADDING AND SUBTRACTING POLYNOMIALS:
 When adding and subtracting polynomials, you COMBINE LIKE TERMS.
 Be careful of parentheses and positive or negative signs with the operations.
Exp 1: (3x2 – 4x + 8) + (2x – 7x2 – 5)
Exp 4: (6y2 + 8y4 – 5y) – (9y4 – 7y + 2y2)
Exp 2: (3n2 + 13n3 + 5n) – (7n + 4n3)
Exp 5: (7y2 + 2y – 3) + (2 – 4y + 5y2)
Example 3: (2b2 + 8ab3 + 4b) – (9b – 5ab3)
Exp 6: (3x2 + 5x + 2) – (4 – 2x) + (5x2 + 7)
PRACTICE PROBLEMS: Simplify each expression
2. ( 3 x  5)  ( 2 x  3)
 2x  3  2x 2  7x  9
1.
x2
3.
( 2 x  3)  (4 x  3)
4.
(2 x 2  2 x  4)  ( x 2  3 x  7)
5.
(3a 2  a  4)  (a 2  2a  1)
6.
( t 2  1)  ( 2t  3)
7.
( 2 x 2  3)  ( x 2  2 x  1)
8.
(2 x 2  5 xy  3 y 2 )  (8 x 2  7 y 2 )
9.
( z 2  2z  5)  ( 3 z 2  z  4)
10.
( 4m  3n )  ( 2n  5m )
Find the PERIMETER of the shape.
Equation: Perimeter = Sum of all the sides
3 – 2x
4x - 8
3a - b
3a - b
11 + y
3a - b
2y – 3x - 3
9x – 3y + 2
12 + 5x + 7y
7 + 3x
3b – 4a + 5
6 + 2a
6 + 2a
4z + 3
5x2 – 2
4z + 3
3b – 4a + 5
Find the sum or difference:
1) (x3 - 7x + 4x2 – 2) – (2x2 – 9x + 4)
2) (3a + 2b – 7c) + (6b – 4a + 9c)
Word Problems:
1) Bob mowed (2x2 + 5x – 3) yards on Monday, (4x – 7) yards on Tuesday, and (3x2 + 10)
yards on Wednesday.
a. How many yards did he mow in the three days?
b. If Bob mowed 14x2 + 12x – 3 yards total for the entire week, how many yards did
he mow during the rest of the week?
2) Molly has (4x + 10) dollars and Ron has (-5x + 20) dollars.
a. How much money do they have altogether?
b. How much more money does Molly have than Ron?
POLYNOMIALS: Multiplication of Monomial and Polynomial
DISTRIBUTIVE PROPERTY REVIEW
1) -4 (2 – 6x )
2) 3 (5p + q – 3r)
3) -2 (-x - 7y)
SIMPLIFYING PRACTICE PROBLEMS:
1) (4x + 7x)3
2) 12z – 5z + 9z2
3) -7 (– 6m + 11m)
4) 4(11 – 3x)
5) – 5(5a – 3b – 6)
6) -2(x2 - 8x + 3x3 – 6)
7) 9x – 4(6 – 3x)
8) 5(3b – 2a) – 7b
9) 12 + 3(7x + 2)
10) 6(4y + 3z) – 11z
11) 5 + 2(4m – 7n) + 9n
12) 12 –7(3 – 5r) + 8r