Add, Subtract and Multiply Polynomials Chapter 5.3 Add, Subtract and Multiply Polynomials

Combine Like Terms Using Addition! Adding Polynomials 𝑥 3 −2 𝑥 2 +4𝑥+8 −3 𝑥 3 + 𝑥 2 −12𝑥−5 Adding Vertically −2 𝑥 3 −𝑥 2 −8𝑥 +3 Adding Horizontally 𝑥 3 −2 𝑥 2 +4𝑥+8 + −3 𝑥 3 + 𝑥 2 −12𝑥−5 = 𝑥 3 + −3 𝑥 3 −2 𝑥 2 + 𝑥 2 +4𝑥+(−12𝑥)+8 + −5 = Combine Like Terms Using Addition! +

Subtracting Polynomials 𝑥 3 −2 𝑥 2 +4𝑥+8 −3 𝑥 3 + 𝑥 2 −12𝑥−5 Subtracting Vertically 4 𝑥 3 −3𝑥 2 +16𝑥 +13 Subtracting Horizontally 𝑥 3 −2 𝑥 2 +4𝑥+8 − −3 𝑥 3 + 𝑥 2 −12𝑥−5 = 𝑥 3 + +3 𝑥 3 −2 𝑥 2 + − 𝑥 2 +4𝑥+(+12𝑥)+8 + +5 = Change the signs of the second polynomial & Combine Like Terms Using Addition! −

Subtract Horizontally You Try Add Vertically Add Horizontally 2𝑥 3 −5 𝑥 2 +3𝑥−9 𝑥 3 + 6𝑥 2 +11 Subtract Vertically Subtract Horizontally

Multiply one term with all the others. Multiplying Polynomials −2 𝑥 2 +3𝑥−6 𝑥−2 Multiplying Vertically +4𝑥 2 −6𝑥 +12 −2𝑥 3 +3𝑥 2 −6𝑥 −2𝑥 3 +7𝑥 2 −12𝑥 +12 Multiply one term with all the others. × Multiply the next term with all the others. + Combine Like Terms Using Addition!

Multiplying Polynomials −2 𝑥 2 +3𝑥−6 𝑥−2 Multiplying Horizontally (𝑥−2)×(−2 𝑥 2 +3𝑥−6) −2 𝑥 3 +3 𝑥 2 −6𝑥 +4 𝑥 2 −3𝑥−6

Multiplying Binomials (𝑥−2)(𝑥+3)(𝑥+1) Multiplying Horizontally 𝑥 2 −2𝑥+3𝑥−6 𝑥 2 +𝑥−6 𝑥+1 𝑥 2 +𝑥−6 𝑥 3 + 𝑥 2 −6𝑥+ 𝑥 2 +𝑥−6 𝑥 3 + 2𝑥 2 −5𝑥+−6