Polynomials Worksheet #1, Study Guides, Projects, Research of Algebra

REVIEW:Polynomial Operations. I will be able to add, subtract, multiply, and divide polynomials. Name. Per. Part 1: Classify each as M (monomial), ...

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REVIEW:Polynomial Operations ______________________________
I will be able to add, subtract, multiply, and divide polynomials. Name Per
Part 1: Classify each as M (monomial), B (binomial), T (trinomial), P (polynomial), or C (constant).
1).______
12 x
2).______
1117 2x
3).______
7328 23 xxx
4).______
130
5).______
1074 2 aa
6).______
1210 3 xx
Part 2: Order of Operations and Fractions
7.) 4 + 2 x 12 6 8 = 8.) 9 3 + 6 x 2 = 9.) 3 + 4 6 + 2 x 35 =
10.)
2
7+3
7=
11.)
4
5+1
2=
12.)
3
1
5
3
Part 3: Add these polynomials. Only combine things that are alike (have the same exponent).
12.) (
13.) (
)181519()764 22 xxxx
14.)
)51719()131520(22 xxxx
15.)
)141510()49( 4556 xxxx
Part 4: Subtract these polynomials.
18.) (6x + 14) - (9x + 5) 20.) (19x2 + 9x + 16) - (5x2 + 12x + 7)
21.) (17x2 + 7x - 14) - (-6x2 - 5x - 18) 22.) (-18x2 + 4x - 16) - (15x2 + 4x 1)
Part 5: Use the distributive property to find the product (multiply).
29.)
)72(6 2 xx
30.)
)1(4 xx
30.)
)5(
2 xx
31.) 3x²(4x³ 5x + 10) 32.)
1223 2 xxx
Part 6: Use the distributive property to find the product (multiply).
33. (x 3)(x + 4) 34. (2x + 4)(2x + 3) 35. (x 7)(x 6) 36. (3x 1)(x + 5)
37. (x + 5)(x2 6x + 3) 38. (2x 3)(4x2 + 8x 2) 39. (2x 1)2 40. (4x+3)2
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REVIEW:Polynomial Operations ______________________________ I will be able to add, subtract, multiply, and divide polynomials. Name Per

Part 1: Classify each as M (monomial), B (binomial), T (trinomial), P (polynomial), or C (constant).

1).______ 2 x  1 2).______ 17 x^2  11 3).______ 8 x^3  2 x^2  3 x  7

4).______  130 5).______ 4 a^2  7 a  10 6).______ 10 x^3  2 x  1

Part 2: Order of Operations and Fractions 7.) 4 + 2 x 12  6 – 8 = 8.) 9  3 + 6 x 2 = 9.) 3 + 4 – 6 + 2 x 35 =

10.)^2

= 11.)^4

Part 3: Add these polynomials. Only combine things that are alike (have the same exponent).

12.) ( (^19) x^2  12 x  12 )( 7 x^2  10 x  13 ) 13.) ( 4 x^2  6 x  7 )( 19 x^2  15 x  18 )

14.) ( 20 x^2  15 x  13 )( 19 x^2  17 x  5 ) 15.)( 9 x^6  4 x^5 )( 10 x^5  15 x^4  14 )

Part 4: Subtract these polynomials. 18.) (6x + 14) - (9x + 5) 20.) (19x^2 + 9x + 16) - (5x^2 + 12x + 7)

21.) (17x^2 + 7x - 14) - (-6x^2 - 5x - 18) 22.) (-18x^2 + 4x - 16) - (15x^2 + 4x – 1)

Part 5: Use the distributive property to find the product (multiply). 29.) 6 ( x^2  2 x  7 ) 30.) 4 x ( 1  x ) 30.) x^2 ( x  5 )

31.) 3x²(4x³ – 5x + 10) 32.) 3 x  x^2  2 x  12 

Part 6: Use the distributive property to find the product (multiply).

  1. (x – 3)(x + 4) 34. (2x + 4)(2x + 3) 35. (x – 7)(x – 6) 36. (3x – 1)(x + 5)
  2. (x + 5)(x^2 – 6x + 3) 38. (2x – 3)(4x^2 + 8x – 2) 39. (2x – 1)^2 40. (4x+3)^2

REVIEW:Polynomial Operations KEY ______________________________ I will be able to add, subtract, multiply, and divide polynomials. Name Per

Part 1: Classify each as M (monomial), B (binomial), T (trinomial), P (polynomial), or C (constant).

1).____B__ 2 x  1 2).____B__ 17 x^2  11 3).P 8 x^3  2 x^2  3 x  7

4).C  130 5).____T__ 4 a^2  7 a  10 6).__T____ 10 x^3  2 x  1

Part 2: Order of Operations and Fractions 7.) 4 + 2 x 12  6 – 8 = 8.) 9  3 + 6 x 2 = 9.) 3 + 4 – 6 + 2 x 35 = 0 15 71

10.)^2

=5/7 11.)^4

Part 3: Add these polynomials. Only combine things that are alike (have the same exponent).

12.)

2 2 2

x x x x x x

2 2 2

x x x x x x

2 2 2

x x x x x x

6 5 5 4 6 5 4

x x x x x x x

Part 4: Subtract these polynomials. 18.) (6x + 14) - (9x + 5) 20.) (19x^2 + 9x + 16) - (5x^2 + 12x + 7) -3x + 9 14x^2 – 3x + 9

21.) (17x^2 + 7x - 14) - (-6x^2 - 5x - 18) 22.) (-18x^2 + 4x - 16) - (15x^2 + 4x – 1) 23x^2 + 12x + 4 -33x^2 – 15

Part 5: Use the distributive property to find the product (multiply).

29.)

2 2

x x x x

30.)^ 4 (1^2 )

x x x x

2 3 2

x x x x

31.) 3x²(4x³ – 5x + 10) 32.) 3 x  x^2  2 x  12 

12x^5 – 15x^3 + 30x^2 -3x^3 + 6x^2 – 36x Part 6: Use the distributive property to find the product (multiply).

  1. (x – 3)(x + 4) 34. (2x + 4)(2x + 3) 35. (x – 7)(x – 6) 36. (3x – 1)(x + 5) X^2 + x – 12 4x^2 +14x + 12 x^2 – 13x + 42 3x^2 + 14x – 5
  2. (x + 5)(x^2 – 6x + 3) 38. (2x – 3)(4x^2 + 8x – 2) 39. (2x – 1)^2 40. (4x+3)^2 X^3 – x^2 - 27x + 15 8x^3 + 4x^2 – 28x + 6 4x^2 – 4x + 1 16x^2 + 24x + 9