1) P(x) = P(0) + P(1)x + P(2)x2
Plug in 1 for x to get: |
| |
P(1) = P(0) + P(1) + P(2) | __ | Subtract P(1) from both sides of the equation |
0 = P(0) + P(2) |
| Subtract P(2) from both sides |
-P(2) = P(0) |
|
Plug in -1 for x to get:
P(-1) = P(0) - P(1) + P(2) |
__ | Since P(-1) = 1 we can substitute 1 in for P(-1) |
1 = P(0) - P(1) + P(2) | Add P(1) to both sides and subtract 1 from both sides. | |
P(1) = P(0) + P(2) - 1 |
| Substitute 0 in for P(0) + P(2) |
P(1) = -1 |
Plug in 2 for x to get:
P(2) = P(0) + 2P(1) + 4P(2) | __
| Substitute -1 in for P(1) and subsitute -P(2) in for P(0) |
P(2) = -P(2) + 2(-1) + 4P(2) | Simplify the right side. | |
P(2) = 3P(2) - 2 |
| Subtract 3P(2) from both sides. |
-2P(2) = -2 | Divide both sides by -2 | |
P(2) = 1 |
| |
Now we can find P(0): |
| |
P(0) = -P(2) Substitute 1 in for P(2) | ||
P(0) = -1 |
|
So we have found that P(x) = -1 - x + x2