Factoring Trinomials Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Factor x2+5x+6x^2 + 5x + 6.

Solution

  1. 1
    Step 1: Find two numbers that multiply to 66 and add to 55.
  2. 2
    Step 2: 2×3=62 \times 3 = 6 and 2+3=52 + 3 = 5. The numbers are 2 and 3.
  3. 3
    Step 3: Factor: (x+2)(x+3)(x + 2)(x + 3).
  4. 4
    Check: (x+2)(x+3)=x2+3x+2x+6=x2+5x+6(x+2)(x+3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6 ✓

Answer

(x+2)(x+3)(x + 2)(x + 3)
For x2+bx+cx^2 + bx + c, find two numbers p,qp, q where pq=cpq = c and p+q=bp + q = b. Then factor as (x+p)(x+q)(x+p)(x+q). This reverses the FOIL multiplication process.

About Factoring Trinomials

Factoring a trinomial of the form ax2+bx+cax^2 + bx + c into a product of two binomials by finding two numbers that multiply to acac and add to bb.

Learn more about Factoring Trinomials →

More Factoring Trinomials Examples

Example 2 hard

Factor [formula] using the AC method.

Example 3 easy

Factor [formula].

Example 4 medium

Factor [formula].

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