Symmetric Polynomials and Polynomial Manipulations - Mastering AMC 10/12

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In this video, we will cover a cool trick to solve symmetric polynomials easily and polynomials manipulations, which is constructing a different polynomial with roots that are reciprocals, more or less by a certain number, etc of another polynomial.

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For more practice, watch the AMC 10/12 Fundamentals Classes here:

If you need a refresher on the fundamentals, check out:
1. AMC 8 Fundamentals:

2. AMC 8 Advanced:

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AMC 10, AMC10, AMC 12, AMC12, AMC 10 Preparation, AMC 10 Crash Course, AMC 10 Concepts, AMC 12 Preparation, AMC 12 Crash Course, AMC 12 Concepts, AMC 10 Review, AMC 12 Review, Number Theory, Primes, Factors Competition math, number of factors, sum of factors, product of factors, AMC 10 number theory, AMC 12 number theory, diophantine equations, divisibility competition math, Area of a Triangle, Similar Triangles, Cyclic Quadrilateral, Power of a point, 3D Geo, Polygons, Coordinate Geometry, Trigonometry, Logarithms, Complex Numbers, Inequalities, Floor and Ceiling Functions, Generating Functions

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Can the variables be different but the coefficient are same like a5 = a4

saurabhsuman

For the complicated polynomial, how could I notice that it’s a symmetrical polynomial?

naturalsustainable

I recognize some stuff from volume 2. I also want to get through precalc, recap intermediate cp, and do vol 2, so do I need to do a lot of exercises or is mostly reading still helpful?

proximitymath

Symmetric Polynomials and Polynomial Manipulations - Mastering AMC 10/12

Symmetric Polynomials and Polynomial Manipulations - Mastering AMC 10/12

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