Topic 1: Multiplying binomials with leading coefficients of 1
  1. Multiply the binomials (x + 3)(x + 5).
  1. Multiply the binomials (x - 4)(x + 7).
Topic 2: Factoring a quadratic with leading coefficient 1
  1. Factor the quadratic x² + 5x + 6.
  1. Factor the quadratic x² - 7x + 12.
Topic 3: Factoring a perfect square trinomial with leading coefficient 1
  1. Factor the trinomial x² + 6x + 9.
  1. Factor the trinomial x² - 8x + 16.
Topic 4: Factoring a difference of squares in one variable: Basic
  1. Factor the expression x² - 25.
  1. Factor the expression x² - 49.
Topic 5: Solving an equation written in factored form
  1. Solve the equation (x + 2)(x - 3) = 0.
  2. Solve the equation (x - 5)(x + 1) = 0.
Topic 6: Finding the roots of a quadratic equation of the form ax² + bx = 0
  1. Find the roots of the equation 2x² + 8x = 0.
  1. Find the roots of the equation 3x² - 12x = 0.
Topic 7: Finding the roots of a quadratic equation with leading coefficient greater than 1
  1. Find the roots of the equation 2x² + 4x - 6 = 0.
  1. Find the roots of the equation 2x² + 9x - 5= 0.
Topic 8: Solving a quadratic equation needing simplification
  1. Solve the equation 2x² + 10 = 6x + 2.
\
  1. Solve the equation 3x² - 12 = 5x - 4.
Topic 9: Solving an equation of the form x² = a using the square root property
  1. Solve the equation x² = 16.
  1. Solve the equation x² = 25.
Topic 10: Solving a quadratic equation using the square root property: Exact answers, basic
  1. Solve the equation (x - 3)² = 9.
  1. Solve the equation (x + 2)² = 4.
Topic 11: Solving a quadratic equation using the square root property: Exact answers, advanced
  1. Solve the equation 2(x - 1)² = 18.
  1. Solve the equation 3(x + 4)² = 27.
Topic 12: Completing the square
  1. Complete the square for the expression x² + 10x.
  1. Complete the square for the expression x² - 6x.
Topic 13: Solving a quadratic equation by completing the square: Exact answers
  1. Solve the equation x² + 8x - 5 = 0 by completing the square.
  1. Solve the equation x² - 10x + 12 = 0 by completing the square.
Topic 14: Applying the quadratic formula: Exact answers
  1. Solve the equation 2x² + 5x - 2 = 0 using the quadratic formula.
  1. Solve the equation 3x² - 5x + 1 = 0 using the quadratic formula.
Topic 15: Solving a word problem using a quadratic equation with irrational roots
  1. A ball is thrown upward with an initial velocity of 32 ft/s from a height of 5 ft. The height h (in feet) after t seconds is given by h = -16t² + 32t + 5. Find the times when the ball is 10 ft above the ground.
  1. A rectangular garden has an area of 60 square feet, and its length is 5 feet more than its width. Find the dimensions of the garden.