Factoring Quadratic Expression: x² + 5x + 4

Objective

To factor the quadratic expression into the form (x + a)(x + b).

Steps to Factor

1. Identify the Expression

   • Given: x² + 5x + 4

2. Setting Up the Problem

   • We want: (x + a)(x + b)
   • Conditions:
     • a * b = 4 (product)
     • a + b = 5 (sum)

3. Find Pairs of Numbers

   • Possible pairs that multiply to 4:
     • (1, 4)
     • (2, 2)

4. Check Sums of Pairs

   • 1 + 4 = 5
   • 2 + 2 = 4
   • Only the pair (1, 4) meets the requirement for sum.

5. Fill in the Blanks

   • Therefore, a = 1 and b = 4
   • The factored form is: (x + 1)(x + 4)

Verification via FOIL

• Use the FOIL method to multiply back:
  • F (First): x * x = x²
  • O (Outside): x * 4 = 4x
  • I (Inside): 1 * x = 1x
  • L (Last): 1 * 4 = 4
  • Combine: x² + 4x + 1x + 4 = x² + 5x + 4

Final Answer

• The factored form of the expression x² + 5x + 4 is:
  • (x + 1)(x + 4)