Question

已知多项式x^2+px+12在给定整数p的条件下可以分解成两个一次因式的积.

Answer 1

1.

12 = ab,所以

p 可能取

1 + 12 = 13

-1 - 12 = -13

3 + 4 = 7

-3 - 4 = -7

2 + 6 = 8

-2 - 6 = -8.

2.

p=13

由ab=12,a+b=13 得

x^2+13x+12 = (x+1)(x+12).