Topic 4 of 6
Polynomials & Factoring
Control exponents, multiply cleanly, and recognize the factor patterns that make higher-degree algebra manageable.
01Algebra · Concept explainerExponent rules that come from counting factorsThe rules are compressed descriptions of repeated multiplication. Knowing where they come from prevents powers from spreading across sums illegally.02Algebra · Method guideMultiplying polynomials without losing a termEvery term in one factor multiplies every term in the other. Organize the products, then combine like terms once.03Algebra · Method guideFactor the greatest common factor before anything fancyThe GCF is the largest expression dividing every term. Removing it first exposes the smaller polynomial that actually needs attention.04Algebra · Method guideFactoring trinomials: use product and sum, not random guessingFor x² + bx + c, find two numbers with product c and sum b. For ax² + bx + c, split the middle term using product ac.05Algebra · Decision guideDifference of squares or perfect-square trinomial?Recognize the pattern from term count, signs, square roots, and the middle coefficient—then expand to confirm rather than trusting appearance alone.