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.
分析:根据题目的条件,先将多项式凑成完全平方的形式,再根据实际情况解答.
解答: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+(
3 |
2 |
3 |
2 |
=(a+
3 |
2 |
121 |
4 |
=(a+
3 |
2 |
11 |
2 |
3 |
2 |
11 |
2 |
=(a-4)(a+7);
(3)x2-(2n+1)x+n2+n,
=x2-(2n+1)x+(n+
1 |
2 |
1 |
2 |
=(x-n-
1 |
2 |
1 |
2 |
=(x-n-
1 |
2 |
1 |
2 |
1 |
2 |
1 |
2 |
=(x-n-1)(x-n).
点评:本题考查了公式法分解因式,是信息给予题,主要渗透配方思想,读懂题目信息是解题的关键.
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