HONORS ALGEBRA 2 - CHAPTER 5 REVIEW

HONORS ALGEBRA 2 - CHAPTER 5 REVIEW

Name: ________________________________________ Date: ________________________ Hour: __________

SECTION 1: Evaluate each numerical expression or simplify each variable expression. Write

your answers as fractions, not decimals.

1) (63)2

2)

3)

4) 57 (54)-3

5) x5 x3

6) (3y2)-4

7) w0z-3

8)

SECTION 2: Decide whether the function is a polynomial function (YES/NO). If it is, write the

function in standard form (SF) and state the degree (D), type (T), and leading coefficient (LC). If it is not, circle the part of the equation that makes the function not a polynomial.

9) f(x) = 2x ? 15 + 3x2 + x4 YES / NO

10) f(x) = 4x4 ? 6x2 + 7x -3 ? 5

YES / NO

SF: ____________________________________ SF: ____________________________________ D: ______ T: ________________ LC: _______ D: ______ T: ________________ LC: _______

11 f(x) = 9x2 ? 4x ? 8x3 ? 1 YES / NO

12) f(x) = x3 + x + 7 ? 8x2

YES / NO

SF: ____________________________________ SF: ____________________________________

D: ______ T: ________________ LC: _______ D: ______ T: ________________ LC: _______

SECTION 3: Use Direct Substitution to evaluate the function for the given value of x.

13) f(x) = x4 ? 4x2 + 3x + 5, for x = -2

14) f(x) = -5x3 ? 8x2 + 7x ? 12, for x = -3

SECTION 4: Use Synthetic Substitution to evaluate the function for the given value of x.

15) f(x) = x4 ? 6x2 + 3x ? 8, for x = 5

16) f(x) = -3x2 ? 2x4 + 5x ? 6 + x3, for x = -1

SECTION 5: Add, subtract, or multiply the polynomials.

17) (5x2 + 3x + 9) + (7x2 ? 1)

18) (2x3 + 11x2 ? 4) ? (4x2 + x)

19) (3x2 + 5)(x2 ? 4x)

20) (2x2 ? 6x + 5)(x2 + 9)

21) (x ? 4)(x3 ? 5x2 + 9x + 10)

22) (-3x2 ? x + 5)(x2 + 4x ? 8)

SECTION 6: Factor each polynomial using difference of two cubes or sum of two cubes.

23) f(x) = x3 + 512 _________________________________________________________________

24) f(x) = 8x3 ? 343 ________________________________________________________________

25) f(x) = 54x3 + 250 _______________________________________________________________

SECTION 7: Find all the zeros of each polynomial function with factor by grouping.

26) f(x) = 2x3 ? 5x2 + 12x - 30

27) f(x) = 6x3 ? 4x2 ? 9x + 6

SECTION 8: Find all the zeros of each polynomial function by getting the polynomial into

quadratic form.

28) f(x) = 2x3 ? 10x2 ? 48x

29) f(x) = 3x5 ? 21x3 ? 54x

SECTION 9: Divide the polynomials using Long Division.

30) (x2 ? 8x + 3) ? (x + 2)

31) (x3 + 6x2 ? 8) ? (x2 ? 3)

SECTION 10: Divide the polynomials using Synthetic Division.

32) (x3 + 12x2 + 31x + 11) ? (x + 4)

33) (2x4 ? 9x2 ? 16x ? 22) ? (x ? 3)

SECTION 11: Use Synthetic Division to factor the polynomial given that f(k) = 0, and then find

all the zeros of the function.

34) f(x) = 3x3 ? 7x2 ? 22x + 8, f(4) = 0

35) f(x) = x3 + 2x2 + 8x + 16, f(-2) = 0

SECTION 12: List all the possible rational zeros of each polynomial function.

36) f(x) = x3 ? 5x2 ? 7x + 20 ___________________________________________________________ 37) f(x) = 2x4 + 8x2 ? 9x ? 36 ___________________________________________________________ 38) f(x) = 5x4 ? 7x3 + x ? 21 _____________________________________________________________

SECTION 13: List all the possible rational zeros and then use Synthetic Division to factor the

polynomial and find all the zeros.

39) f(x) = x3 ? 3x2 ? 6x + 8

40) f(x) = x4 ? 3x3 + 2x2 ? 18x ? 24

SECTION 14: Write a polynomial function given that it has the following solutions.

41) solutions: 1, 3, -5

42) solutions: -1, -4, 2, 6

43) solutions: -3, ?4i

44) solutions: ?6i, 2 ? i

SECTION 15: Describe the end behavior of each polynomial function.

45) f(x) = 3x4 - 6x3 + 8x ? 10

46) f(x) = -2x3 ? 6x2 + 3x +4

47) f(x) = x5 + 5x3 ? 6x2 + 11

f(x) ____ as x -

f(x) ____ as x -

f(x) ____ as x -

f(x) ____ as x +

f(x) ____ as x +

f(x) ____ as x +

SECTION 16: Make a table of values to graph each polynomial function. Use the end behavior as a guide.

48) f(x) = -2x4 + 7x2

49) f(x) = x3 + x2 ? 5x + 1

SECTION 17: Use the x-intercepts and the local minimum and local maximum values to graph

the polynomial function.

50) f(x) = (x ? 3)(x + 2)(x + 7)

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download