题目内容
阅读理解我们知道:多项式a2+6a+9可以写成(a+3)2的形式,这就是将多项式a2+6a+9因式分解.当一个多项式(如a2+6a+8)不能写成两数和(或差)的平方的形式时,我们通常采用下面的方法:a2+6a+8=(a+3)2﹣1=(a+2)(a+4).请仿照上面的方法,将下列各式因式分解:
(1)x2﹣6x﹣27;
(2)a2+3a﹣28;
(3)x2﹣(2n+1)x+n2+n.
(1)x2﹣6x﹣27;
(2)a2+3a﹣28;
(3)x2﹣(2n+1)x+n2+n.
解:(1)x2﹣6x﹣27,
=x2﹣6x+9﹣36,
=(x﹣3)2﹣62,
=(x﹣3﹣6)(x﹣3+6),
=(x+3)(x﹣9);
(2)a2+3a﹣28,
=a2+3a+()2﹣()2﹣28,
=(a+)2﹣,
=(a+﹣)(a++),
=(a﹣4)(a+7);
(3)x2﹣(2n+1)x+n2+n,
=x2﹣(2n+1)x+(n+)2﹣(n+)2+n2+n,
=(x﹣n﹣)2﹣()2,
=(x﹣n﹣﹣)(x﹣n+),
=(x﹣n﹣1)(x﹣n).
=x2﹣6x+9﹣36,
=(x﹣3)2﹣62,
=(x﹣3﹣6)(x﹣3+6),
=(x+3)(x﹣9);
(2)a2+3a﹣28,
=a2+3a+()2﹣()2﹣28,
=(a+)2﹣,
=(a+﹣)(a++),
=(a﹣4)(a+7);
(3)x2﹣(2n+1)x+n2+n,
=x2﹣(2n+1)x+(n+)2﹣(n+)2+n2+n,
=(x﹣n﹣)2﹣()2,
=(x﹣n﹣﹣)(x﹣n+),
=(x﹣n﹣1)(x﹣n).
练习册系列答案
相关题目