Add and Subtract Polynomials

(​Review from Algebra 1)

• I TEACH the same

• You LEARN the same

MGSE9-12.A.APR.1 Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations

​Learning goal: I can add, subtract, and multiply polynomials.

​How to Add/Subtract Polynomials

Three Steps: Sum (F + G)x and Difference (F - G)x

• Start with: (Difference case: just distribute a parentheses for 2nd term)

  (F + G)x = F(x) + G(x) or (F - G)x = F(x) - G(x)

• Place the like terms together (according to the degree of x)

• Combine the like terms by adding or subtracting them

​Examples (F + G)[x]

​Given F(x) = 2x² + 6x + 5 and G(x) = 3x² - 2x - 1. Find (F + G)x?

​S1: Start with: (F + G)x = F(x)+ G(x)

​= 2x² + 6x + 5 + 3x² - 2x - 1

​Examples (F + G)[x]

​Given F(x) = 2x² + 6x + 5 and G(x) = 3x² - 2x - 1. Find (F + G)x?

​S1: Start with: (F + G)x = F(x)+ G(x)

​= 2x² + 6x + 5 + 3x² - 2x - 1

​= 2x² + 3x² + 6x - 2x + 5 - 1

​S2: Place the like term together:

​Examples (F + G)[x]

​Given F(x) = 2x² + 6x + 5 and G(x) = 3x² - 2x - 1. Find (F + G)x?

​S1: Start with: (F + G)x = F(x)+ G(x)

​= 2x² + 6x + 5 + 3x² - 2x - 1

​= 2x² + 3x² + 6x - 2x + 5 - 1

​S2: Place the like term together:

​S3: Combine like term:

​= 5x² + 4x + 4

​= (2 + 3)x² + (6 - 2)x + (5 - 1)