Factoring Intuition Math Example 2

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Example 2

medium
Find two numbers that multiply to −15-15 and add to 22.

Solution

  1. 1
    Since the product is negative, one number is positive and one is negative.
  2. 2
    Factor pairs of 15: (1,15),(3,5)(1,15), (3,5).
  3. 3
    Try 55 and −3-3: 5×(−3)=−155 \times (-3) = -15 and 5+(−3)=25 + (-3) = 2 ✓

Answer

5 and −35 \text{ and } -3
When the product is negative, the two numbers have opposite signs. The larger absolute value gets the sign that matches the sum.

About Factoring Intuition

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

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More Factoring Intuition Examples

Example 1 easy

What two numbers multiply to 12 and add to 7?

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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