The polynomial of one variable second degree of af of a standard type² + bf + c is called a square trinomial. One of transformations of a square trinomial consists in its decomposition on multipliers. Decomposition has an appearance (f – f1) (f – f2), and f1 and f2 are solutions of a quadratic equation of a polynomial.
Instruction
1. Write down a square trinomial. The formula for decomposition on multipliers of the first degree is presented in the form by a (f – f1) (f – f2). And yes – coefficient of the equation, f1 and f2 – the solution of a quadratic equation of our polynomial. Thus, for decomposition it is required to solve the polynomial equation.
2. Present a square trinomial in af equation form² + bf + c = 0. Solve this equation. For this purpose find a discriminant on formula D = b²? 4ac. If the discriminant turned out negative, then this equation has no decisions and the square trinomial cannot be factorized.
3. If the discriminant is more or is equal to zero, then decisions exist. Allocate a root square of value of a discriminant. Write down the turned-out value in the form of the QD variable.
4. Substitute the known parameters in a formula of definition of roots: k1 = (-b+QD) / 2a and k2 = (-b-QD) / 2a. If D = 0, the root is one.
5. Write down decomposition of a square trinomial. For this purpose we substitute the turned-out roots in formula a (f – f1) (f – f2).