Solving a Quadratic by Factoring

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1. 1. The problem0:00
   Solving a Quadratic by Factoring

   $x^2 - 5x + 6 = 0$
2. 2. Find the pair0:12
   $$x^2 - 5x + 6 = 0$$

   Two numbers with product $6$ and sum $-5$

3. 3. Factor and solve0:28
   1. $$(x - 2)(x - 3) = 0$$
   2. $$x - 2 = 0 \quad \text{or} \quad x - 3 = 0$$
      zero-product property
   3. $$x = 2 \quad \text{or} \quad x = 3$$
4. 4. See it on the graph0:42

5. 5. Check0:54
   1. $$2^2 - 5(2) + 6 = 4 - 10 + 6 = 0$$
   2. $$3^2 - 5(3) + 6 = 9 - 15 + 6 = 0$$
6. 6. Recap1:07
   • ✓Get $0$ on one side.
   • ✓Find two numbers with product $c$ and sum $b$.
   • ✓Set each factor to $0$, then check.

Solve by factoring, completing the square or the quadratic formula; use the discriminant.

• Quadratic Equation Calculator: try the same kind of problem with your own numbers.
• Complete the Square Calculator: try the same kind of problem with your own numbers.
• Factoring Calculator: try the same kind of problem with your own numbers.
• More algebra practice problems
• Quadratic Equations Study Guide (study guide)
• Algebra calculators and topics
• Step-by-step solver: check your own answer with hints.

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