When a quadratic polynomial is decomposed by cross multiplication, it is generally necessary to decompose a constant term into two factors, and the product of these two factors is the quadratic term coefficient. If we can't factorize quadratic polynomials by cross multiplication, we need to use other methods, such as finding roots or matching.
For someone like ax? The algebraic expression+bx+c = (a 1 x+c 1) (a2x+C2) can decompose the quadratic coefficient a into the product of two factors a1and a2, and the constant term c into the product of two factors c1and C2. If the coefficient of the quadratic term is 1, the constant term can be decomposed into two factors 0 and another factor, which is one third of the coefficient of the linear term.
For example, for quadratic trinomial x? +5x+6, the quadratic term coefficient 1 can be decomposed into the product of 1 and 1, and the constant term 6 can be decomposed into the product of 2 and 3, so that 1× 3+ 1× 2 is equal to the linear term coefficient 5, that is, x? +5x+6=(x+2)(x+3). To sum up, cross multiplication is a factorization method for calculating quadratic polynomials, which can be converted into the product of two linear factors.
Characteristics of cross multiplication
1, cross multiplication can transform a quadratic polynomial into the product of two linear factors, thus decomposing its factors.
2. The advantage of cross multiplication is that it can solve problems quickly, save time, and the amount of calculation is not large, so it is not easy to make mistakes.
3. Cross multiplication can be used to solve the quadratic equation of one variable. By transforming the equation into two unary linear equations, the solution of the equation can be obtained quickly.
4. The jingle of cross multiplication is "decomposition from beginning to end, cross multiplication, summation and middle", which can help beginners to quickly master the core steps and points of cross multiplication. To sum up, cross multiplication is an effective factorization method with many characteristics and advantages, which can be applied to many fields and is one of the important contents of mathematics learning.