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乘法公式(x+a)(x+b)=x~2+(a+b)x+ab的逆运算,就是x~2+(a+b)x+ab=(x+a)(x+b),对于这个二次三项式,二次项分解成x·x,常数项分解成a·b,排成图1,交叉相乘再相加等于一次项,这就是用十字相乘法因式分解.对于二次三项式ax~2+bx+c,如果能把ax分解成两个一次项的积,即ax~2=(a_1x)·(a_2x),把常数项c分解成两个数的积,即c_1·c_2,并且交叉相乘的二积之和正好等于一次项,即a_1c_2x+a_2c_1x=bx,如图2,就可以把这个二次三项式分解因式为ax~2+bx+c=(a_1x+c_1)(a_2x+c_2).例1把10(x+2)~2-29(x+2)+10分
The inverse of the multiplication formula (x + a) (x + b) = x ~ 2 + (a + b) x + ab is x ~ 2 + (a + b) x + ab = (x + a) + b). For this quadratic, the quadratic term is decomposed into x · x and the constant term is decomposed into a · b, which is plotted in Figure 1. The cross-wise multiplication is equal to the one-time term, which is multiplied by the cross For the quadratic formula ax ~ 2 + bx + c, if ax can be decomposed into the product of two first-order terms ax ~ 2 = (a_1x) · (a_2x), the constant term c is decomposed The product of two numbers, c_1 · c_2, and the cross-product of the two products exactly equal to the first term, that is, a_1c_2x + a_2c_1x = bx, as shown in Figure 2, this quadratic decomposition factor is ax2 + bx + c = (a_1x + c_1) (a_2x + c_2). Example 1 10 (x + 2) to 2-29 (x + 2)