Infinite Algebra 2 - Unit 1A Review 1

Secondary Math 3

Name___________________________________ ID: 1

©W l2l0x1Z5R LKZurtAaq HS]olfKtMw_abr]el jLjL\CR.D x oAplnlQ hrtiPgJhwttsO yrvewsYeMrvvXendv.

Unit 1A Review 1

Date________________ Period____

List the terms in each expression. Then list all coefficients, variables, and term degrees. 1) 3m 5 + 2m 2 + 4

2) - 2m

Write a polynomial function using the given terms. Determine the degree of each polynomial function. 3) 7 x, - 6 x 4 , 5 x 2 , 8 x 3

The figure below is divided into separate parts with each area written within that part. Find an expression that represents the total area of the figure. All units are in square inches. 4)

Simplify each expression. Write your answer in standard form. 5) ( a - a 3 + 5 ) + ( 2a + 6a 5 - a 3 )

6) ( 3n 3 - 3n - 8 ) - ( 7n - 8n 3 - 3 - 2n 4 )

7) ( 8r 3 - 3 ) - ( 3 + r 3 + r + 4r 5 )

8) ( 7 x 5 + 1 - 8 x 4 + 5 x 3 ) + ( 2 x 2 - 7 x 4 + 6 x 5 - 5 )

9) ( 2 x + 5 )( 6 x - 4 )

10) ( 2n + 6 )( 2n 2 + n + 4 )

11) ( x + 6 )

2

12) ( 5m 2 + 3m - 1 )( 3m 2 + 4m - 6 )

Find the perimeter and area of a rectangle with each given length and width. All measurements are given in centimeters. (Include units in your answer.) 13) length: 4 x + 2 width: x 2 - 7

14) length: - 2 x + 10 width: 5 x - 12

Worksheet by Kuta Software LLC

-1-

©x O2_0i1F5\ QKQuntGaL ASyomfJtYwVarrves TLyL_Cz.a e GArlblJ nrwi[gwhDtSsb ardeksfelrEvZeydk.t w mMZaxdLeH iwLijtjhO \IanffRiwn]ictUeL gAhldguevbIrmaz M2a.

Factor each. 15) x 3 - 8

16) 64 x 3 + 1

17) x 2 - 64

18) 81 x 2 - 64

Describe the end behavior of each function. 19) f (x) = x 2 + 6 x + 8

20) f (x) = - x 5 + 4 x 3 - 5 x - 4

Sketch the general shape of each function. 21) f (x) = x 3 - 13 x 2 + 56 x - 80

22) f (x) = - x 4 + 3 x 2 - 2 x + 1

Divide. 23) ( 4 p 3 + 29 p 2 - 32 p - 61 ) ¸ ( p + 8 )

24) ( x 4 - x 3 - 7 x 2 - 3 x + 18 ) ¸ ( x - 3 )

25) ( 5 p 3 - 44 p 2 - 45 p + 13 ) ¸ ( 5 p + 6 )

State if the given binomial is a factor of the given polynomial. 26) ( n 3 - 2n 2 - 12n + 9 ) ¸ ( n + 3 )

Use synthetic substitution to evaluate each function at the given value. 27) f (a) = 6a 3 - 28a 2 + 14a + 10 at a = 4

28) f (n) = n 3 - 11n 2 + 34n - 9 at n = 5

29) The area in square feet of a rectangular garden can be expressed as the product of the garden's length and width, or A ( x ) = 3 x 2 + 13 x + 14. If the width of the garden is (x + 2) feet, what is the length of the garden?

State the possible rational zeros for each function. 30) f (x) = 4 x 3 - 4 x 2 - x + 1

31) f (x) = 4 x 3 - 9 x 2 + 6 x - 1

Find all zeros. 32) f (x) = 2 x 3 - 5 x 2 + x + 2

33) f (x) = 2 x 3 - x 2 - 2 x + 1

Worksheet by Kuta Software LLC

-2-

©x k2Z0B1K5[ gKruVtAaY [S^oSfBtewyasrDeW wLkLnCX.[ F [AtlolT DrViugZhlt_sE WrVeMsdeDrQvBeadb.L H wMya]dgeV hw_iYtYhy zIGndfpiqnyiptKeI NAzlXgaevbXrTaO G2f.