Math Final Review

Polynomials

100

Add (3x² + 5x) + (4x² + 6)

7x² + 5x + 6

200

Multiply (2x + 7)(4x — 5)

8x² + 18x — 35

300

Factor x² — 25

(x + 5)(x — 5)

400

Find the roots: 0 = 3x(x — 4)(x — 6)

0, 4, and 6

Rational Expressions/Equations/Etc.

100

Add and simplify:

(2/4x) + (6/4x)

2/x

200

Multiply and simplify: 

(5ab²/6b²) x (12a²b²/5ab³)

2a²/b

300

Identify any excluded values. Then simplify the expression: (2x + 10)/(4x + 20)

excluded value: -5

Simplified expression: 1/2

400

Solve for x:

(6/5 — x) = (x/x + 5)

x = -6 or 5

Logarithms

100

Write into logarithmic form:

2³ = 8

log₂8 = 3

200

Write into exponential form:

log₁₀100 = 2

10² = 100

300

Simplify log₃27²

6

400

Simplify:

ln e^{5x + 7}

5x + 7

Linear/Quadratic Equations/formula

100

Solve: 5x + 25 = 45

X = 4

200

Give the y-intercept of the equation y = 5x -6

-6

300

Solve: 3x² — 7x + 2

(7 + 5)/6 or (7 — 5)/6

400

Write a quadratic equation whose roots are 3

x² — 6x + 9

Miscellaneous

100

Add 2i + 5i

7i

200

Write the equation of a circle whose center point is (3,4) and has a radius of 5.

(x — 3)² + (y — 4)² = 25

300

Find the 7th term of the sequence: 4, 16, 64,…

16,384

400

Expand (x + y)³

x³ + 3x²y + 3xy² +y³