Factoring
I suppose you mean factoring the polynomial. You can check by multiplying the factors - the result should be the original polynomial.
Yes.
It means finding numbers (constant terms), or polynomials of the same or smaller order that multiply together to give the original polynomial.
Yes. Factoring a polynomial means to separate it into smaller factors, which, when multiplied together, give you the original polynomial.
If there is no common factor then the polynomial cannot be factorised. If there is no common factor then the polynomial cannot be factorised. If there is no common factor then the polynomial cannot be factorised. If there is no common factor then the polynomial cannot be factorised.
mn(n4-m2)mn(n2+m)(n2-m)
A strategy that would be appropriate in factoring polynomials with 4 terms would be by grouping where you first determine if the polynomial can be factored by a group.
A parabola is a graph of a 2nd degree polynomial function. Two graph a parabola, you must factor the polynomial equation and solve for the roots and the vertex. If factoring doesn't work, use the quadratic equation.
An expression that completely divides a given polynomial without leaving a remainder is called a factor of the polynomial. This means that when the polynomial is divided by the factor, the result is another polynomial with no remainder. Factors of a polynomial can be found by using methods such as long division, synthetic division, or factoring techniques like grouping, GCF (greatest common factor), or special patterns.
Polynomial factoring is often taught in order to develop a particular thinking skill: deconstruction. There are many times when we have an object, concept, or apparatus that we want to understand more clearly, and so we need to take it apart. A good example of this in computer programming would be reverse engineering, where one would be trying to understand a program, given that you know what the program does. Factoring is precisely that; you look at an expression, study its characteristics, and attempt to unravel it into components. It's a problem of analysis! Remember that many math concepts are like this when applied to other fields--- it's a pattern of thought that you are learning!
Factoring a polynomial with 5 or more terms is very hard and in general impossible using only algebraic numbers. The best strategy here is to guess some 'obvious' solutions and reduce to a fourth or lower order polynomial.