# Questions tagged [solving-polynomials]

For questions about solving polynomials. Polynomials are expressions like $15x^3 - 14x^2 + 8$. Questions tagged with this concern common operations on polynomials… like adding, multiplying, polynomial long division, factoring and solving for roots.

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### Algebra 2 textbooks that incorrectly claim that all solutions of polynomial equations can be found

Over the years I have occasionally encountered a number of Algebra 2 textbooks that make an incorrect (or at very least extremely misleading) claim along the lines that "all solutions of a polynomial ...
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### Factoring quadratics where the coefficient on the $x^2$ term does not equal 1

so we are working through various methods of factoring quadratic equations and the students seem comfortable factoring basic quadratics such as: $$x^2 - 7x + 12 = 0$$ by finding the factors of $12$ ...
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In Secondary education in Australia, the general outline for introducing techniques to solve the quadratic equation $$x^2+bx+c=0$$ is first to introduce the idea to find two numbers $p$ and $q$ such ...
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### In which course should we teach solving general cubic and quartic equations?

I am guessing solving general cubic and quartic equations should be taught in a course somewhere between precalculus and Galois theory, though personally I do not recall learning this topic ever in ...
331 views

### Why is polynomial factorization over the integers part of secondary school curricula?

By "polynomial factorization over the integers", I mean problems and solutions like the following: Problem: Find a factorization into irreducible polynomials for $24x^2 +x - 10$ and ...
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### Should Eisenstein’s criterion be taught in high-school?

Eisenstein’s criterion: If you have a polynomial with integer coefficients (and a non-zero constant term) and there’s some prime number $p$ such that $p$ goes into every coefficient but not ...
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### How to work with polynomials in difficult classes?

I am currently teaching a very difficult class, with young people (16 years old) who are deeply unmotivated and restless. I should work with them with polynomials, but I'm having a troublesome time; ...
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### Is it a problem if a senior student majoring in mathematics could not prove the quadratic formula?

According to a recent experiment conducted by user Steven Gubkin, nearly one half of his students in a senior level Real Analysis course do not have any idea how to prove the quadratic formula. Is ...