将以下每个二次三项式分解为因式：
问题1. 2x 2 + 5x + 3
解决方案：
Given:
2x2 + 5x + 3
The coefficient of x2 = 2
The coefficient of x = 5
Constant term = 3
Split the centre term, that is ‘5’ into two parts such that their sum p+q is 5 and product pq = 2 × 3 is 6
So, we write the middle term 5x as 2x + 3x
2x2 + 5x + 3 = 2x2 + 2x + 3x + 3
= 2x (x + 1) + 3 (x + 1)
= (2x + 3) (x + 1)
问题2：2个2 – 3倍- 2
解决方案：
Given:
2x2 – 3x – 2
The coefficient of x2 = 2
The coefficient of x = -3
Constant term = -2
So, we write the middle term -3x as -4x + x
2x2 – 3x – 2 = 2x2 – 4x + x – 2
= 2x (x – 2) + 1 (x – 2)
= (x – 2) (2x + 1)
问题3. 3x 2 + 10x + 3
解决方案：
Given:
3x2 + 10x + 3
The coefficient of x2 = 3
The coefficient of x = 10
Constant term = 3
So, we write the middle term 10x as 9x + x
3x2 + 10x + 3 = 3x2 + 9x + x + 3
= 3x (x + 3) + 1 (x + 3)
= (3x + 1) (x + 3)
问题4. 7x – 6 – 2x 2
解决方案：
Given:
7x – 6 – 2x2
– 2x2 + 7x – 6
2x2 – 7x + 6
The coefficient of x2 = 2
The coefficient of x = -7
Constant term = 6
So, we write the middle term -7x as -4x – 3x
2x2 – 7x + 6 = 2x2 – 4x – 3x + 6
= 2x (x – 2) – 3 (x – 2)
= (x – 2) (2x – 3)
问题5. 7x 2 – 19x – 6
解决方案：
Given:
7x2 – 19x – 6
The coefficient of x2 = 7
The coefficient of x = -19
Constant term = -6
So, we write the middle term -19x as 2x – 21x
7x2 – 19x – 6 = 7x2 + 2x – 21x – 6
= x (7x + 2) – 3 (7x + 2)
= (7x + 2) (x – 3)
问题6：28 – 31x – 5x 2
解决方案：
Given:
28 – 31x – 5x2
– 5x2 -31x + 28
5x2 + 31x – 28
The coefficient of x2 = 5
The coefficient of x = 31
Constant term = -28
So, we write the middle term 31x as -4x + 35x
5x2 + 31x – 28 = 5x2 – 4x + 35x – 28
= x (5x – 4) + 7 (5x – 4)
= (x + 7) (5x – 4)
问题7. 3 + 23岁– 8岁2
解决方案：
Given:
3 + 23y – 8y2
– 8y2 + 23y + 3
8y2 – 23y – 3
The coefficient of y2 = 8
The coefficient of y = -23
Constant term = -3
So, we write the middle term -23y as -24y + y
8y2 – 23y – 3 = 8y2 – 24y + y – 3
= 8y (y – 3) + 1 (y – 3)
= (8y + 1) (y – 3)
问题8. 11x 2 – 54x + 63
解决方案：
Given:
11x2 – 54x + 63
The coefficient of x2 = 11
The coefficient of x = -54
Constant term = 63
So, we write the middle term -54x as -33x – 21x
11x2 – 54x + 63 = 11x2 – 33x – 21x – 63
= 11x (x – 3) – 21 (x – 3)
= (11x – 21) (x – 3)
问题9. 7x – 6x 2 + 20
解决方案：
Given:
7x – 6x2 + 20
– 6x2 + 7x + 20
6x2 – 7x – 20
The coefficient of x2 = 6
The coefficient of x = -7
Constant term = -20
So, we write the middle term -7x as -15x + 8x
6x2 – 7x – 20 = 6x2 – 15x + 8x – 20
= 3x (2x – 5) + 4 (2x – 5)
= (3x + 4) (2x – 5)
问题10. 3x 2 + 22x + 35
解决方案：
Given:
3x2 + 22x + 35
The coefficient of x2 = 3
The coefficient of x = 22
Constant term = 35
So, we write the middle term 22x as 15x + 7x
3x2 + 22x + 35 = 3x2 + 15x + 7x + 35
= 3x (x + 5) + 7 (x + 5)
= (3x + 7) (x+ 5)