A polynomial is transformed into the product of several algebraic expressions in a value domain (real value domain decomposition, that is, all terms are real numbers). The deformation of this formula is called factorization of this polynomial, which is also called factorization of this polynomial.

In mathematics, the algebraic expression formed by adding several monomials is called polynomial (if there is subtraction, subtracting a number is equal to adding its inverse).

Each monomial in a polynomial is called a polynomial term, and the highest degree of these monomials is the degree of this polynomial. Items without letters in polynomials are called constant terms.

Factorization method:

Factorization does not apply to all cubic equations, but only to some cubic equations. For most cubic equations, only by finding their roots can they be factorized.

Of course, the solution of factorization is very simple, and the cubic equation is simplified directly. For example, if the equation X 3-X = 0 is solved, the left factor is decomposed to get x(x+ 1)(x- 1)=0, and three roots of the equation are obtained: X 1 = 0, X2 = 1, and X3 =-65438.

Another alternative method:

For the general cubic equation, the equation is transformed into a special type of x+px+q=0 by using the formula and substitution mentioned above. Let x=z-p/3z, and substitute it for simplification to get: z-p/27z+q=0. Let z=w, and substitute it to get: w+p/27w+q=0.

This is actually a quadratic equation about W. Solve W, and then solve Z and X in turn.

Solution of jinsheng formula;

Cubic equation is widely used. Although there is a famous Kardan formula and the corresponding discrimination method to solve the univariate cubic equation with root sign, it is complicated and lacks intuition.

Shenjin Fan derived a set of simple root-seeking formulas of cubic equation with one variable directly expressed by A, B, C and D, and established a new discriminant method.

Jinsheng formula:

The unary cubic equation ax 3+bx 2+CX+d = 0, (a, b, c, d ∈ r, a≠0).

Multiple root discriminant: a = B2-3ac；; B = 9adC = c 2-3bd BC, and the total discriminant is δ = b 2-4ac. When A=B=0, the formula of gold enrichment is x1= x2 = x3 =-b/(3a) =-c/b =-3d/c.

When δ = b 2-4ac >; At 0, the formula of golden age is: x1= (-b-(y1) (1/3)-(y2) (1/3))/(3a).

X2，3 =(-2 b+(y 1)( 1/3)+(y2)( 1/3))/(6a)i3( 1/2)((y 65438+)

When δ = b 2-4ac = 0, the golden formula ③: x1=-b/a+k; X2 = x3 =-k/2, where K=B/A, (A≠0). When δ = b 2-4ac0,-1.