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Adding polynomials
Adding polynomials involves combining like terms. There are two ways to add polynomial: horizontal method and vertical method.
For instance, to add
2x2 + 3x - 1, and
x2 - x + 5
1) Using horizontal method, we write the addition as
2x2 + 3x - 1 + x2 - x + 5
Rearrange the terms so that like terms are next to each other
2x2 + x2 + 3x - x -1 + 5
Combining like terms, we have
3x2 + 2x + 4
2) Using vertical method, we write the two polynomials in a column so
that the like terms are in line with each other.
| 2x2 | +3x | -1 |
| + x2 | -x | +5 |
| 3x2 | +2x | +4 |
So the sum is 3x2 + 2x +4
Example 1
Add x3 + 2x2 + 3 and x2 - 4x - 5
Solution:
1) horizontal method:
x3 + 2x2 + 3 + x2 - 4x - 5
= x3 + 2x2 + x2 - 4x + 3 - 5
rearrange so that like terms are next to each
other
= x3 + 3x2 - 4x -2
combining like terms
2) vertical method
| x3 | +2x2 | +3 | |
| + | x2 | -4x | -5 |
| x3 | +3x2 | -4x | -2 |
So the sum is x3 + 3x2 - 4x -2
Example 2
Add x2 + y2 + xy + 2x - 3y + 2 and -2y2 - 3xy
+ x - 3
Solution:
1) horizontal method:
x2 + y2 + xy + 2x - 3y + 2 + (-2y2 - 3xy
+ x - 3)
= x2 + y2 + xy + 2x - 3y + 2 - 2y2 -
3xy + x - 3
= x2 + y2 - 2y2 + xy - 3xy + 2x + x - 3y + 2
- 3
= x2 - y2 - 2xy + 3x - 3y - 1
2) vertical method
| x2 | +y2 | +xy | +2x | -3y | +2 |
| + | -2y2 | -3xy | +x | -3 | |
| x2 | -y2 | -2xy | +3x | -3y | -1 |
So the sum is x2 - y2 - 2xy + 3x - 3y - 1