Subtracting Polynomials
When we subtract polynomials, we subtract the like terms. Because a - b = a +
(-b), we can subtract by adding the opposite of the second polynomial to the
first polynomial. Remember that a negative sign in fron of parentheses changes
the sign of each term in the parentheses. For example,
-(x2 - 2x + 8) = -x2 + 2x - 8.
Polynomials can be subtracted horizontally or vertically, as shown in the
next example.
Subtracting polynomials
Perform the indicated operation.
a) (x2 - 5x - 3) - (4x2 + 8x - 9)
b) (4y3 - 3y + 2) - (5y2 -7y - 6)
Solution
| a) (x2 - 5x - 3) - (4x2 + 8x - 9) |
= x2 - 5x - 3 - 4x2 - 8x + 9 |
Change signs. |
| |
= -3x2 - 13x + 6 |
Add. |
b) To subtract 5y2 - 7y -6 from 4y3 - 3y + 2 vertically,
we line up the like terms as we do for addition:
|
4y3 |
|
- 3y |
+ 2 |
|
- |
(5y2 |
- 7y |
- 6) |
Now change the signs of 5y2 - 7y - 6 and add the like terms:
|
4y3 |
|
- 3y |
+ 2 |
| |
-5y2 |
+
7y |
+
6) |
|
4y3 |
-5y2 |
+ 4y |
+ 8 |
Caution
when adding or subtracting polynomials vertically, be sure to line up the
like terms.
|
