MAT097 Chapters 3 and 4 Review

Exponents

100

Use the product rule to simplify the following:

x⁵ * x⁹

x¹⁴

200

Use the product rule to simplify the following:

(4x³)(9x⁵)

36x⁸

300

Use the power rules to simplify the following:

(y³)¹¹

y³³

400

Using the quotient rule, simplify the following:

(x¹²y⁵) / (x⁸y⁴)

x⁴y

Polynomials

100

Add the following polynomials:

(5x³ - 3x + 7) + (4x³ - 2x² +10x)

9x³ - 2x² + 7x + 7

200

Subtrat the following polynomials:

(4x³ + 9) - (-8x³ - 13)

12x³ + 22

300

Multiply the following polynomials: 

(3x² - 4)(2x³ + 5)

6x⁵ - 8x³ + 15x² - 20

400

Multiply the following polynomials:

(y-6)(y+6)

y² - 36

Factor by Grouping

100

Factor out the GCF from the polynomial:

y³ + 2y

y(y² + 2)

200

Factor out the GCF of the polynomial:

16y⁵ + 8y³ - 12y

4y(4y⁴ + 2y² - 3)

300

Factor out the GCF from the polynomial:

x(y² - 2) + 3(y² - 2)

(y² - 2)(x + 3)

400

Factor by grouping:

8y² - 12y + 10y - 15

(4y + 5)(2y - 3)

Factoring trinomials

100

Factor the trinomial:

x² + 11x + 30

(x + 5)(x + 6)

200

Factor the trinomial:

x² - 13x + 30

(x + 10)(x + 3)

300

Complete the factored form:

3x² + 8x + 4 = (3x + 2) (        )

(3x + 2)(x + 2)

400

Factor the trinomial:

2x² + 20x - 22

Hint: Look for GCF first

2(x - 1)(x + 11)

Solving Quadratic Equations

100

Solve for x in the following equation:

(x - 1)(x + 4) =0

x = 1, -4

200

Solve for x in the following equation:

5x(x - 15) = 0

x = 0, 15

300

Solve for x in the following equation:

x² - 7x = 0

x = 0, 7

400

Solve for x in the following equation:

x² = 25

x = -5, 5