Maths factoring
By Christine Wong Pui Lei
Example 1 :
Factor 2x3 - x2 - 5x -2 =0
Answer :
(Ax2 - Bx + C)(Nx - O) = ANx3 - (AO + BN)x2 + (BO + CN)x - CO
Take note of the + / - sign.
AN=2
AO + BN = 1
BO + CN = -5
CO =2
| A= | | BN | BO |
| B= | | 0 | -9 |
| C= | | AO | CN |
| N= | | | |
| O= | |
1 |
4 |
| ANCO= 1x4 | | 1 | -5 |
| ANCO= 2x2 | | | |
| ANCO=-1X-4 | | | |
| ANCO=-2x-2 | | | |
| A=2 | | BN | BO |
| B=-3 | | -3 0 | -6 -9 |
| C=1 | | AO | CN |
| N=1 | | | |
| O=2 | |
4 1 |
1 4 |
| ANCO= 1x4 | | 1 | -5 |
| ANCO= 2x2 | | | |
| ANCO=-1X-4 | | | |
| ANCO=-2x-2 | | | |
(2x2 +3x +1)(x -2)=0
(2x +1)(x + 1)(x-2)=0
Note : There are another 2 sets of figures can fulfill the chart.
| A=2 | | BN | BO |
| B=3 | | 3 | -3 |
| C=-2 | | AO | CN |
| N=1 | | | |
| O=-1 | |
-2 |
-2 |
| ANCO= 1x4 | | 1 | -5 |
| ANCO= 2x2 | | | |
| ANCO=-1X-4 | | | |
| ANCO=-2x-2 | | | |
| A=1 | | BN | BO |
| B=1 | | 2 | -1 |
| C=-2 | | AO | CN |
| N=2 | | | |
| O=-1 | |
-1 |
-4 |
| ANCO= 1x4 | | 1 | -5 |
| ANCO= 2x2 | | | |
| ANCO=-1X-4 | | | |
| ANCO=-2x-2 | | | |
Note : You may get the answer for some equation on your 1st try.
Refer to the example below.
Example 2 :
Factor 2x3 + x2 - 2x -1 =0
Answer :
(Ax2 - Bx + C)(Nx - O) = ANx3 - (AO + BN)x2 + (BO + CN)x - CO
AN=2
AO + BN = -1
BO + CN = -2
CO =1
| A=1 | | BN | BO |
| B=0 | | 0 | 0 |
| C=-1 | | AO | CN |
| N=2 | | | |
| O=-1 | |
-1 |
-2 |
| ANCO= 1x2 | | -1 | -2 |
| ANCO=-1X-2 | | | |
(x2 -1)(2x + 1)=0
(x +1)(x - 1)(2x+ 1)=0
For power 4 equation, the chart is as follow :
(Ax3 - Bx2 + Cx - D)(Nx - O) = ANx4 - (AO + BN)x3 + (BO + CN)x2 - (CO + DN)x + DO
| A= | | BN | CO | | BO | CN |
| B= | | | |
| C= | |
|
|
|
|
|
| D= | | AO | DN |
BNCO |
|
BO+CN |
| N= | | | |
| O= | |
|
|
| ANDO= | | AO+BN | CO+DN |