Factoring Polynomials

Factor each expression:

 

a) x^{3}+8

sum of two cubes → a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})

a=x,\ b^{3}=8\rightarrow \sqrt[3]{b^3}=\sqrt[3]{8}\rightarrow b=2

x^{3}+8=(x+2)(x^{2}-2x+2^{2})

x^{3}+8=(x+2)(x^{2}-2x+4)

 

b) 8ax+4bx+6ay+3by+4cx+3cy

  1. Group the terms
    • (8ax+4bx+4cx)+(6ay+3by+3cy)
  2. Factor out GCF
    • 4x(2a+b+c)+3y(2a+b+c)
  3. Distributive property
    • (4x+3y)(2a+b+c)