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 basic mathematics image

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 2x2 + -3x + 4 from 3x2 + 5x + 8

Step #1:

Rewrite the problem

3x2 + 5x + 8 − (2x2 + -3x + 4)

Replace minus sign by + -

3x2 + 5x + 8 + -(2x2 + -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

3x2 + 5x + 8 + -(2x2 + -3x + 4) = 3x2 + 5x + 8 + -2x2 + 3x + -4

Combine all like terms. You could use parenthesis to keep things organized

3x2 + 5x + 8 + -2x2 + 3x + -4     = (3x2 + -2x2 ) + (5x + 3x) + 8 + -4

                                                 = (3 + -2) x2 + (5 + 3)x + 4

                                                 = 1x2 + (8)x + 4

                                                 = x2 + 8x + 4

Example #2:


Subtract 4x2 + 6x + 5 from -8x2 + -4x + 8

Step #1:

Rewrite the problem

-8x2 + -4x + 8 − (4x2 + 6x + 5)

Replace minus sign by + -

-8x2 + -4x + 8 + -(4x2 + 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

-8x2 + -4x + 8 + -(4x2 + 6x + 5) = -8x2 + -4x + 8 + -4x2 + -6x + -5

Combine all like terms. You could use parenthesis to keep things organized

-8x2 + -4x + 8 + -4x2 + -6x + -5 = (-8x2 + -4x2 ) + (-4x + -6x) + 8 + -5

                                                 = (-8 + -4) x2 + (-4 + 6)x + 3

                                                 = (-12)x2 + (-10)x + 3

                                                 = -12x2 + -10x + 3


I did not use algebra tiles for this lesson about subtracting polynomials.

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