Unit 2 Polynomials Test Review

Exponent Rules

100

4x²y²¹ x 3x^-19y^-121

12 / x¹⁷y¹⁰⁰

200

(3x^-3y⁴)^-3

x⁹ / 27y¹²

300

x / (2x^-3)³

x¹⁰ / 8

400

(a ( a x a⁰)^-2) / (5a)²

1 / 25a³

500

(14a³²b^-4c¹⁶d^-20 / 42a⁴⁰b⁸c²⁰)⁴

1 / 81a³²b⁴⁸c¹⁶d⁸⁰

Classification, Substitution, & End Behavior

100

Classify this polynomial by the number of terms and degree

180x²⁷+679x³³+90102x³¹

33^rd Degree Trinomial

200

Is this a polynomial? Explain your answer.

f(x) = 21x⁴ + -19x^-3 + (pi)² + 214x - 9

NO!

Negative Exponent

300

Using direct or synthetic substitution, solve this polynomial when x = 3

9x³ + 2x² + 17x + 1

313

400

Fill in the blanks for the end behavior statement for this polynomial: 10x⁷ + x² - 13x⁴ - 7x⁸

As x --> ∞, f(x) --> _____

As x --> -∞, f(x) --> _____

As x --> ∞, f(x) --> -∞

As x --> -∞, f(x) --> -∞

500

Graph -x³ + x² + x - 1

(0,-1)

(1,0)         (-1,0)

(2,-3)        (-2,9)

Adding, Subtracting, Multiplying

100

(14x³ + 12x² - 9) + (-12x² + 13x³ - 2x - 32)

27x³ - 2x - 41

200

21480x⁰ + 23

24

300

(11x² + 14x - 90) - (9x² - 14x - 45)

2x² + 28x + 135

400

(19x+15)²

361x² + 570x + 225

500

(ab + 10)³

a³b³ + 30a²b² + 300ab + 1000

Factoring

100

Factor & Solve: 81x² - 36

(9x + 6)(9x - 6)

x = 2/3, -2/3

200

Factor & Solve: x³ + x² + x + 1

(x² + 1)(x + 1)

x = i, -i, -1

300

Factor: 6x⁶ - 5x³ - 4

(2x³ + 1)(3x³ - 4)

400

Factor & Solve: 2y⁵ - 18y³

2y³(y + 3)(y - 3)

y = 0, 0, 0, -3, 3

500

Factor & Solve: x³ - 512

(x - 8)(x² + 8x + 64)

x = 8, -4 + 4i √3, -4 - 4i√3

Dividing

100

What's the mistake?

2 |  3    14     -9       2        5

   |_____6___40___62___128_ 

      3     20    31      64     133

There is no mistake!

200

(x³ + 5x² - 7x + 2) / (x - 2)

x² + 7x + 7 + 16/x - 2

300

(x⁴ + 3x³ - 8x² + 4x) / (x - 3)

x³ + 6x² + 10x + 34 + 102/x - 3

400

(2x⁴ + x³ + x - 1) / (x² + 2x + 1)

2x² - 3x + 4 + -4x - 5/x² + 2x + 1

500

Factor & Solve:

(x³ - x² - 17x - 15) ----- x = -1

(x - 5)(x + 3)(x + 1)

x = 5, -3, -1