MAT097 Final Review

Quadratics/Factoring

100

Factor 12xy⁴ - 8x²y

4xy(3y³ - 2x)

200

Factor x² - 10x + 16

(x - 2)(x - 8)

300

Solve for x

x² - 3x - 4 = 0

x = -1, 4

400

Solve for x

7x² = 2x + 9

x = -1, 9/7

500

Factor completely

6x³ + 28x³ + 16x

2x(x + 4)(3x + 2)

Functions

100

Is the following relation a function?

{(-14, 22), (22, 19), (-25, 19), (-24, 11), (6, -1)}

Yes

200

For the function f(x) = 7x² - 9x -2  find f(2)

f(2) = 8

300

{(-23, -23), (-16, -8), (19, -9), (-6, -16), (10, 4), (-20, 0)}

Find the domain and range of the function above

Domain: -23, -16, 19, -6, 10, -20

Range: -23, -8, -9, -16, 4, 0

400

For the function h(x) = 6x - 3 find h(x - 4)

h(x) = 6x - 27

500

For the function g(x) = 4 - 2x find g(3x + 5) - g(8)

-6x + 6

Radicals

100

Simplify   sqrt(36d¹⁸u¹⁴)

6d⁹u⁷

200

Simplify sqrt(60x⁹y²)

2x⁴y sqrt(15x)

300

Multiply (2 - sqrt(x))(8 + 4sqrt(x))

-4x + 16

400

Divide and simplify, rationalize the denominator if necessary

sqrt(5x⁵)/sqrt(10x³)

xsqrt(2)/2

500

3sqrt(12ab²) + 3b sqrt(75a) - 3sqrt(27ab²)

12b sqrt(3a)

Rationals

100

Determine the domain

4/(x² + 9x + 20)

x does not equal -5, -4

200

Simplify

(x² + 8x + 15)/(x² + 9)

(x + 5)/(x - 3)

300

Multiply and simplify

(10x + 100)/(9x + 108)  (x² + 23x + 132)/(x² + 16x + 60)

10(x + 11) / 9(x + 6)

400

3/x-2 + 5/x+2 + 6/x² - 4

(8x+2)/((x+2)(x-2))

500

Solve for x

2/(x - 4) + 3 = 5/(x - 4)

x = 5

Miscellaneous

100

Solve for x

2 - 6x > 8

x < -1

200

Find the vertex of x² + 4x - 1

(-2, -5)

300

3| 2x + 7 | = 27

x = 1, -8

400

8 + | 4x - 7 | > 17

x < -1/2 or x > 4

500

A toy rocket is shot vertically upward from the ground. Its height in feet from the ground in t seconds is given by  h = -16t² + 96t. What is the maximum height of the rocket?

144