Factoring Intuition Math Example 1

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

Example 1

easy
What two numbers multiply to 12 and add to 7?

Solution

  1. 1
    List factor pairs of 12: (1,12),(2,6),(3,4)(1,12), (2,6), (3,4).
  2. 2
    Check sums: 1+12=131+12=13, 2+6=82+6=8, 3+4=73+4=7 ✓
  3. 3
    The numbers are 3 and 4.

Answer

3 and 43 \text{ and } 4
Factoring intuition is about finding what multiplies together to give an expression. For trinomials x2+bx+cx^2 + bx + c, you need two numbers with product cc and sum bb.

About Factoring Intuition

Understanding factoring as finding what multiplies together to give an expression.

Learn more about Factoring Intuition →

More Factoring Intuition Examples

Example 2 medium

Find two numbers that multiply to [formula] and add to [formula].

Example 3 easy

Find two numbers that multiply to 18 and add to 9.

Example 4 hard

Find two numbers that multiply to [formula] and add to [formula].

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