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14. 已知$a^2 - a - 2 = 0$,则代数式$a^3 - 2a^2 - a + 2025 =$
2023
.
答案：
14.2023
15. 新定义:对于任意实数$x$,都有$f(x) = ax^2 + bx$,若$f(1) = 5,f(2) = 12$,则将$f(x^2 - 4)$的结果分解因式后是
x²(x + 2)(x - 2)
.
答案：
15.x²(x + 2)(x - 2)
16. (8 分)分解因式.
(1)$12abc - 2bc^2$.
(2)$2a^3 - 12a^2 + 18a$.
(3)$9a(x - y) + 3b(x - y)$.
(4)$(x + y)^2 + 2(x + y) + 1$.
(1)$12abc - 2bc^2$.
(2)$2a^3 - 12a^2 + 18a$.
(3)$9a(x - y) + 3b(x - y)$.
(4)$(x + y)^2 + 2(x + y) + 1$.
答案：
16.
(1)2bc(6a - c).
(2)2a(a - 3)².
(3)3(x - y)(3a + b).
(4)(x + y + 1)².
(1)2bc(6a - c).
(2)2a(a - 3)².
(3)3(x - y)(3a + b).
(4)(x + y + 1)².
17. (6 分)先分解因式,再求值:$9(a - b)^2 - 4(a + b)^2$,其中$a = \frac{1}{5},b = -1$.
答案：
17.解:原式=(5a - b)(a - 5b).当a = $\frac{1}{5}$,b = -1 时，原式 = $\frac{52}{5}$.
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