General Factoring and Its Application
5-13Using Factoring to Solve Problems
Overview
Geometry, number, and area problems often lead to quadratic equations you can solve by factoring.
Key ideas
- Write the equation from the problem.
- Move everything to one side; factor.
- Discard answers that don’t fit (e.g., negative length).
Worked examples
Example 1
Problem. A rectangle’s length is 2 more than its width and its area is 24. Find dimensions.
Solution. w(w + 2) = 24 → w^2 + 2w − 24 = 0 → (w + 6)(w − 4) = 0 → w = 4 (reject −6); length = 6.
Practice
Try each one. Click Show answer when ready.
- 1.
Two consecutive integers have a product of 56. Find them.
- 2.
x^2 + 3x = 10. Solve.
- 3.
A rectangle: length is 3 more than width; area = 40. Find dimensions.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
The product of two consecutive positive integers is 132. Find the integers.
- 2.
A rectangle's length is 3 more than its width. The area is 54. Find the dimensions.