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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.

7
votes
4answers
152 views

Beyond cubic polynomials: Applications?

Cubic polynomials are crucially important in computer graphics: for example, cubic Bézier curves/surfaces, and cubic splines, which have many practical applications. Essentially visual continuity ...
9
votes
5answers
316 views

Motivation for polynomial long division

In the U.S. students in grades $\{9,10,11\}$ often learn long division of two polynomials, e.g.: $$ \frac{x^4 + 6x^2 + 2}{x^2 + 5} = x^2 + 1 - \frac{3}{x^2 + 5} \;. $$ I believe it is fair to say that ...
14
votes
4answers
270 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 ...
11
votes
4answers
4k views

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; ...
11
votes
1answer
195 views

Solving linear equations by factoring

I usually teach solving linear equations by balancing both sides e.g. $$\begin{array}{cccc} 2x&+&3&=&5\\ &&\color{red}{-3}&&\color{red}{-3}\\ 2x&&&=&2\\...
15
votes
10answers
2k views

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 $12$ ...
11
votes
6answers
1k views

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 ...
15
votes
6answers
786 views

Factoring quadratic polynomials

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 ...