Algebra

Overview

Algebra problems usually become manageable after finding the right form. Factor expressions, normalize variables, introduce symmetric quantities, and look for hidden convexity or monotonicity.

Checklist

• Try factoring before expanding.
• Identify symmetry in variables or roots.
• Test whether a substitution removes clutter.
• Check equality cases in inequalities.
• Look for polynomial roots, degree constraints, or coefficient comparisons.

Common moves

• Use Vieta’s formulas to connect roots and coefficients.
• Complete the square or apply AM-GM, Cauchy-Schwarz, or Jensen where appropriate.
• Convert a functional equation into special values and substitutions.
• Compare coefficients after proving two polynomials agree on enough points.

Practice problems

Tags: algebra

Problem	Source	Difficulty	Tags
Starter Algebra Problem	Boilerplate	2	algebra, inequalities
Starter Geometry Problem	Boilerplate	2	geometry, algebra