1

Polynomials & Rationals

100

Add: (3x² + 2x - 5) + (2x² - 7x + 4)

5x² - 5x - 1

200

Factor completely: x² - 9

(x - 3)(x + 3)

300

Use the Remainder Theorem to find the remainder when f(x) = x³ - 4x + 1 is divided by x - 2.

f(2) = 8 - 8 + 1 = 1

400

Simplify: (x² - 1)/(x + 1)

x - 1

500

Prove the identity: (x + y)² = x² + 2xy + y²

Expand (x + y)(x + y) = x² + xy + xy + y² = x² + 2xy + y²

Quadratics

100

What is the vertex of the parabola y = (x - 3)² + 2?

(3, 2)

200

Solve: x² - 6x + 9 = 0

x = 3 (multiplicity 2)

300

Use the quadratic formula to solve: x² + 4x + 1 = 0

x = -2 ± √3

400

Simplify: √(-36)

6i

500

Find the focus of the parabola y = (x - 2)² + 1

Focus at (2, 1.25)

Systems & Rational Equations

100

Solve the system: x + y = 5, x - y = 1

x = 3, y = 2

200

Solve: 1/(x+1) + 1/(x-1) = 2/(x² - 1)

All real numbers except x = ±1

300

Solve the system: 2x + y = 4, x - y = 1, x + 2y = 5

x = 1, y = 1, z = 2

400

Is (x + 2)/(x² - 4) = 1/(x - 2) + 1/(x + 2)? Prove algebraically.

Yes, combine right side: common denominator is x² - 4

500

Word problem: If it takes 3 hours for one pump and 6 hours for another, how long to fill the pool together?

2 hours

Polynomial Functions

100

Find the y-intercept of f(x) = x³ - 4x + 2

(0, 2)

200

Is f(x) = x⁴ - x² even, odd, or neither?

Even

300

Describe end behavior: f(x) = -2x⁵ + x³

Left: ↑, Right: ↓

400

Find all real zeros of f(x) = x³ - 6x² + 11x - 6

x = 1, 2, 3

500

Given zeros 2 (multiplicity 2) and -1, find the equation

f(x) = a(x - 2)²(x + 1), a ≠ 0

Exponents & Radicals

100

Simplify: x⁰

1

200

Simplify: (x³)²

x⁶

300

Simplify √(50)

5√2

400

Solve: √(x + 3) = 4

x = 13

500

Rewrite: x^(2/3) as a radical

∛(x²)