Problem
Factor: x² + 5x + 6
📝Step-by-Step Solution
1
Identify what we need
For x² + bx + c, we need two numbers that: multiply to give c (6), AND add to give b (5).
Need: ? × ? = 6 and ? + ? = 5
2
List factor pairs of 6
Factor pairs of 6: (1, 6), (2, 3), (-1, -6), (-2, -3)
3
Find the pair that adds to 5
1 + 6 = 7 ✗, 2 + 3 = 5 ✓. The numbers are 2 and 3!
2 × 3 = 6 ✓ and 2 + 3 = 5 ✓
4
Write as two binomials
x² + 5x + 6 = (x + 2)(x + 3)
x² + 5x + 6 = (x + 2)(x + 3)
5
Check by expanding
(x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6 ✓
✅Final Answer
(x + 2)(x + 3)
Factoring reverses the FOIL method. The factored form helps us solve equations: if x² + 5x + 6 = 0, then (x + 2)(x + 3) = 0, so x = -2 or x = -3. Remember: when c is positive and b is positive, both factors are positive.
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