Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomial Functions
Rational Expressions
Formulas
f(x) = x^2 - 4
g(x) = x^2 - 6x + 8
h(x) = x - 4
(f + g)(x) = 2x^2 - 6x + 4
(h - g)(x) = -x^2 + 7x - 12
(f * h)(x) = x^3 - 4x^2 - 4x + 16
(g / f)(x) = (x - 4) / (x + 2) for x ≠ 2
(h / g)(x) = 1 / (x - 2) for x ≠ 2, 4
Theorems
Distributive Property
Factorization of Polynomials
Suitable Grade Level
Grades 9-12
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