College Algebra Formula Sheet: The Ultimate Guide to Navigating Mathematical Complexities

Conversions
– Angles: 1 degree = (π/180) radians; 1 radian = (180/π) degrees
– Temperature: Celsius to Fahrenheit: F = (9/5)C + 32; Fahrenheit to Celsius: C = (5/9)(F-32)

Algebraic Operations
– Distributive property: a(b + c) = ab + ac
– Commutative property: a + b = b + a; ab = ba
– Associative property: (a + b) + c = a + (b + c); (ab)c = a(bc)

Polynomials
– Standard form: ax^n + bx^(n-1) + … + c
– Degree: The highest exponent of x
– Leading coefficient: The coefficient of the term with the highest exponent
– Zeros: The values of x that make the polynomial equal to zero

Factoring Polynomials
– Quadratic: (ax + b)(cx + d)
– Difference of squares: (a + b)(a – b)
– Trinomial: (x + a)(x + b), (x – a)(x – b), (x^2 + ax + b), (x^2 – ax + b)

Rational Expressions
– Simplifying: Multiply numerator and denominator by the least common multiple (LCM) of the denominators
– Dividing: Invert the divisor and multiply by the dividend

Radical Expressions
– Simplifying: Remove perfect squares from the radicand
– Operations: √(ab) = √a * √b, √(a/b) = √a / √b

Exponent Rules
– a^m * a^n = a^(m + n)
– (a^m)^n = a^(mn)
– a^-m = 1/a^m
– a^0 = 1

Logarithm Rules
– log(ab) = log(a) + log(b)
– log(a/b) = log(a) – log(b)
– log(a^b) = blog(a)

Trigonometry
– Sine: sin(θ) = opposite/hypotenuse
– Cosine: cos(θ) = adjacent/hypotenuse
– Tangent: tan(θ) = opposite/adjacent

Trigonometric Identities
– Pythagorean identity: sin^2(θ) + cos^2(θ) = 1
– Double-angle formulas: sin(2θ) = 2sin(θ)cos(θ), cos(2θ) = cos^2(θ) – sin^2(θ)

Applications
– Engineering: Structural analysis, fluid dynamics, thermodynamics
– Physics: Motion, forces, wave phenomena
– Economics: Modeling demand curves, supply curves, elasticity
– Finance: Interest rates, investment returns, financial planning
– Biology: Population growth, enzyme kinetics, genetics

Tips and Tricks
– Factor first: Factor polynomials before performing other operations.
– Use identities: Utilize trigonometric identities to simplify expressions.
– Be careful with negatives: Be mindful of negative signs when multiplying or dividing.
– Check your answers: Substitute your answers back into the original equation to verify.

Table 1: Algebraic Operations

Table 2: Polynomial Factoring

Table 3: Radical Operations

Table 4: Trigonometric Identities