Cross multiplication can decompose some quadratic trinomials. The key of this method is to decompose the quadratic coefficient A into two parts.
The product of a factor a 1 and a2 a 1? A2, decompose the constant term c into two factors, the product of c 1 and C2? C2, and let a 1c2+a2c 1 happen to be the main term b, then the result can be written directly.
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When using this method to decompose factors, we should pay attention to observation and try to understand that it is essentially the inverse process of binomial multiplication. When the first coefficient is not 1, it often needs to be tested many times, so be sure to pay attention to the sign of each coefficient.
Basic formula: x 2; +(p+q)x+pq=(x+p)(x+q) The so-called cross multiplication is factorization by using the inverse operation of the multiplication formula (X+A) (X+B) = X 2+(A+B) X+AB. For example, put X 2+X 7+.
The constant 12 of the above formula can be decomposed into 3*4, and 3+4 is just equal to the coefficient 7 of the linear term, so
The above formula can be decomposed into: x 2+7x+ 12 = (x+3) (x+4).
Another example: factorization factor: a 2+2a-15. The constant-15 in the above formula can be decomposed into 5 *(3), and 5+(-3) is just equal to the linear coefficient 2, so a 2+2a-15 = (a+5