Do you mean why do why do we factor a polynomial? If so, one reason is to solve equations. Another is to reduce radical expressions by cancelling out factors in the numerator and denominator.
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.
The opposite of expanding expressions is factoring them. While expanding involves distributing and combining like terms to create a polynomial from its factors, factoring breaks down a polynomial into its constituent factors or simpler expressions. This process often reveals the roots or zeros of the polynomial. Both techniques are fundamental in algebra for manipulating and solving equations.
The first step in factoring a polynomial with four terms is to look for a common factor among the terms. If no common factor exists, you can try grouping the terms into two pairs and factor each pair separately. This often reveals a common binomial factor that can be factored out, simplifying the polynomial further.
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.
The zeros of a polynomial are the values of the variable for which the polynomial evaluates to zero. These values are also known as the roots or solutions of the polynomial equation. Finding the zeros is essential for understanding the behavior of the polynomial graph, including its intercepts with the x-axis. The zeros can be determined using various methods, such as factoring, the quadratic formula, or numerical techniques.
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.