Unit 2 Summary

Calculus Readiness · Axiom Academy

SUMMARY Unit 2 Summary: Algebra Fluency You rebuilt the algebraic machinery calculus runs on — factoring, rational expressions, exponents, radicals, equations, inequalities, and functions. Factoring is pattern recognition. GCF, grouping, trinomials, and the special forms a^2-b^2 and turn a sum into a product — and a product is what reveals zeros. Rational expressions are fractions of polynomials. You factor, cancel common factors, and stay alert to the values that make a denominator zero. Exponents and radicals are one language. A radical is just a fractional exponent: , so every radical rule is an exponent rule in disguise. Solving means isolating, with care. Linear, quadratic, rational, and radical equations each balance both sides — but squaring and clearing denominators can introduce extraneous solutions you must check. A function is a rule with a domain. Notation f(x) , domain/range, and piecewise definitions are how you name what a relationship does and where it is allowed to do it. Core Concept Factoring Polynomials Rewriting a polynomial as a product of simpler factors. You pull out a GCF, factor by grouping, match trinomial patterns, and recognize special forms — the difference of squares above, plus the sum and difference of cubes. When to use: any time you need the zeros of an expression, or want to cancel inside a fraction. Watch out for: always check for a GCF first; a^2+b^2 does not factor over the reals. Core Concept Rational Expressions

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