Recomposition Math Example 1

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

Example 1

easy
After decomposing x2+5x+6=(x+2)(x+3)x^2 + 5x + 6 = (x+2)(x+3), recompose to solve x2+5x+6=0x^2+5x+6 = 0.

Solution

  1. 1
    Decomposition gave: x2+5x+6=(x+2)(x+3)x^2+5x+6 = (x+2)(x+3).
  2. 2
    Set the product equal to zero: (x+2)(x+3)=0(x+2)(x+3) = 0.
  3. 3
    Recompose the solution: either x+2=0x+2=0 (giving x=−2x=-2) or x+3=0x+3=0 (giving x=−3x=-3).
  4. 4
    Final answer: x∈{−2,−3}x \in \{-2, -3\}.

Answer

x=−2 or x=−3x = -2 \text{ or } x = -3
Recomposition uses the pieces obtained in decomposition to assemble the final answer. The zero-product property lets us read off solutions directly from the factored form.

About Recomposition

Recomposition is the process of combining simpler parts, sub-results, or solved sub-problems back together to form a complete solution or to understand the whole structure from its pieces.

Learn more about Recomposition →

More Recomposition Examples

Example 2 medium

Partial fractions gave [formula]. Recompose to verify by adding the fractions.

Example 3 easy

You find [formula] and [formula] from solving a system. Recompose by substituting back into both equ

Example 4 medium

Given the identity [formula], recompose: use it to evaluate [formula].

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Related Concepts

Decomposition