Subtracting polynomials
Before, you start this lesson about subtracting polynomials, make sure you have mastered
addition of polynomials
Furthermore, you have to understand how to add and subtract
integers
There is no way around these or you will struggle!
Example #1:
Subtract 2x
^{2} + 3x + 4 from 3x
^{2} + 5x + 8
Step #1:
Rewrite the problem
3x
^{2} + 5x + 8 − (2x
^{2} + 3x + 4)
Replace minus sign by + 
3x
^{2} + 5x + 8 + (2x
^{2} + 3x + 4)
The negative sign will change the sign for every term inside the parenthesis. It is just like taking the opposite
Therefore if something is positive, it will become negative. If it is negative, it will become positive
3x
^{2} + 5x + 8 + (2x
^{2} + 3x + 4) = 3x
^{2} + 5x + 8 + 2x
^{2} + 3x + 4
Combine all like terms. You could use parenthesis to keep things organized
3x
^{2} + 5x + 8 + 2x
^{2} + 3x + 4
= (3x
^{2} + 2x
^{2} ) + (5x + 3x) + 8 + 4
= (3 + 2) x
^{2} + (5 + 3)x + 4
= 1x
^{2} + (8)x + 4
= x
^{2} + 8x + 4
Example #2:
Subtract 4x
^{2} + 6x + 5 from 8x
^{2} + 4x + 8
Step #1:
Rewrite the problem
8x
^{2} + 4x + 8 − (4x
^{2} + 6x + 5)
Replace minus sign by + 
8x
^{2} + 4x + 8 + (4x
^{2} + 6x + 5)
The negative sign will change the sign for every term inside the parenthesis. It is just like taking the opposite
Therefore, if something is positive, it will become negative. If it is negative, it will become positive
8x
^{2} + 4x + 8 + (4x
^{2} + 6x + 5) = 8x
^{2} + 4x + 8 + 4x
^{2} + 6x + 5
Combine all like terms. You could use parenthesis to keep things organized
8x
^{2} + 4x + 8 + 4x
^{2} + 6x + 5
= (8x
^{2} + 4x
^{2} ) + (4x + 6x) + 8 + 5
= (8 + 4) x
^{2} + (4 + 6)x + 3
= (12)x
^{2} + (10)x + 3
= 12x
^{2} + 10x + 3
I did not use algebra tiles for this lesson about subtracting polynomials.
Any problems, use the form
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