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Algebra & Polynomials

Master Algebra with 'Value Putting', 'Symmetry', and 'Degree Check'. Covers Identities, Polynomials, Remainder Theorem, and Linear Equations.

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Model 1: Algebraic Identities

$(a+b)^2 = a^2 + b^2 + 2ab$
$(a+b)^3 = a^3 + b^3 + 3ab(a+b)$
$a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)$
Condition: If $a+b+c=0$ , then $a^3+b^3+c^3 = 3abc$ .

Model 2: Value Putting Strategy

Rule: Denominator $\ne 0$ . Options must be unique.
Golden Values: Try $a=1, b=1, c=0$ or $a=2, b=1, c=-3$ .
Symmetry: If variables are symmetric, try $a=b=c$ .

Model 3: Polynomials & Remainder Theorem

Remainder Theorem: If $P(x)$ is divided by $(x-a)$ , remainder is $P(a)$ .
Factor Theorem: If $P(a) = 0$ , then $(x-a)$ is a factor.
Roots: For $Ax^2+Bx+C=0$ , $\alpha+\beta = -B/A$ , $\alpha\beta = C/A$ .

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