Hw - Polynomial Operations

HW Polynomials, and their Operations

Name ______________________________ Per _______

Part 1: Write the degree of each polynomial in the blank. If the polynomial has a name, write it under the problem. 1).______ 2 x + 1

2).______ 17 x 2 + 11

3).______ 8 x 3 + 2 x 2 + 3 x − 7

4).______ − 130

5).______ 4a 2 + 7 a − 10

6).______ 10 x 3 − 2 x + 1

Part 2: Standard Form of Polynomials 7.) Circle the problems that are in proper standard form. If not in standard form, re-write in standard form. x 3 − 11x 2 a. b. x2 – x4 + 2x2 c. – x5 - 17 d. − 1 + 3 x + 2 x 2 __________ e.

5 - 3x __________

8.

________________________ f. 4x + 5x2 + 8 ____________________

____________

____________________

g. − 3 x + 17 x 4 + 2 x 2

h. 2+ 3x + 4 x 2 + 3x3

___________________

____________________

Given: How many terms are there? ______

What is the leading Coefficient? _______

What is the coefficient of the 3rd term (from R)? ______ What is the degree of the polynomial? _______

What is the constant? _______

What is the leading term? ________

Part 3: REVIEW: Add these polynomials. Only combine like terms (have the same variable exponents). 9.) 14x + 5 +10x + 5

10.)

10x + 12 + 6x + 20

11.) 17 x 2 + 11 + 8 x 2 + 11

12.) ( 19 x 2 + 12 x + 12) + (7 x 2 + 10 x + 13)

13.) ( 4 x 2 − 6 x + 7) + (−19 x 2 − 15x − 18)

14.) (20 x 2 + 15x + 13) + (−19 x 2 + 17 x + 5)

15.) (9 x 6 − 4 x5 ) + (10 x5 − 15x 4 + 14)

Part 4: REVIEW: Subtract these polynomials. 18.) (6x + 14) 19.) (14x2 + 13x + 12) - (9x + 5) - (7x2 + 20x + 4)

21.) (17x2 + 7x - 14) - (-6x2 - 5x - 18)

20.) (19x2 + 9x + 16) - (5x2 + 12x + 7)

22.) (-18x2 + 4x - 16) - (15x2 + 4x - 13)

Part 5: REVIEW: Multiplying Monomials 23.) 2 x(4 x 2 ) 24.) 17 x 2 (2 x5 )

25.)

− 3 x 3 (4 x 2 )

26.) − 12 x 2 (−2 x)

Part 6: REVIEW: Use the distributive property to find the product (multiply the polynomials)). 27.)

4( x + 2)

30.) − x 2 ( x + 5)

28.)

− 3(2 x 2 + 1)

29.) 6( x 2 + 2 x + 7)

31.) 3x(x – 3) (x + 2)

30.)

(

4 x(1 − x)

32.) 3x − x 2 + 2 x − 12

)

Part 7: REVIEW: Use division and distribution to simplify. Remember, the dividing line is a grouping symbol! 33.)

− 15x + 10 5

36.)

14 x3 + 28x 2 − 70 7

6 x 2 + 10 34.) 2

37.)

20 x 4 + 15x 2 5x2

− 18x 2 + 21x 35.) −3

38.)

x 4 + 3x3 + 7 x x