Practice Decomposition in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The strategy of breaking a complex mathematical object or problem into simpler, independent subproblems that can be solved separately.
Divide and conquer: a hard problem of size n becomes n easy problems. Long division, partial fractions, and integration by parts all use decomposition.
Example 1
easyFactorise 12x^2 + 8x - 4 by decomposing the expression into simpler parts.
Example 2
mediumDecompose the partial fraction \dfrac{5x+1}{(x+1)(x-2)} into the form \dfrac{A}{x+1} + \dfrac{B}{x-2}.
Example 3
easyDecompose solving the system 2x + y = 7 and x - y = 2 into steps.
Example 4
mediumDecompose the proof that \sqrt{2} + \sqrt{3} is irrational into logical sub-goals.