➕ Algebra 1 · Quadratics
Solving Quadratics by Factoring cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
The five steps
- Z: Zero on one side
- F: Factor completely (GCF first)
- S: Set each factor to 0
- S: Solve each one
- C: Check in the original equation
Zero-product property
- If A × B = 0, then A = 0 or B = 0
- Works only for a product equal to 0
- For a factor like x + p, the solution is x = −p
Special cases
- (x + 4)2 = 0: one solution, x = −4 (double root)
- 3x(x + 7) = 0: x = 0 or x = −7 (3 gives nothing)
- x2 − 49 = 0: x = 7 or x = −7
- Prime trinomial: use a later method
Graph link
- Solutions = x-intercepts of the parabola
- Two solutions: crosses twice
- Double root: touches once, at the vertex
Watch out
- Never divide both sides by x
- Do not split a product that is not 0
- Reject answers that do not fit the story
Formulas
- Standard form of the equation: ax2 + bx + c = 0, with a ≠ 0
- Zero-product property: If A × B = 0, then A = 0 or B = 0 (or both)
- Difference of squares: a2 − b2 = (a + b)(a − b)
- Perfect square trinomials: a2 + 2ab + b2 = (a + b)2 and a2 − 2ab + b2 = (a − b)2 (each gives a double root)
- Solutions and the graph: Solutions of ax2 + bx + c = 0 = x-intercepts of y = ax2 + bx + c
Solving Quadratics by Factoring cheat sheet from HighSchoolQ.com, for personal study use.