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!
Examples about subtracting polynomials.
Example #1:
Subtract 2x
^{2} + 3x + 4 from 3x
^{2} + 5x + 8
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 of 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
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 of 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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Study also this example in the figure about subtracting polynomials

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