Question

Factor each expression. Show your work. 11. r2 + 12r + 27 12. g2 – 9 13. 2p3 + 6p2 + 3p + 9

Answer 1

11. r^2 + 12r + 27 = (r+3)(r+9)

12. g^2-9 = (g+3)(g-3)

13. 2p^3 + 6p^2 + 3p + 9 = (2p^2+3)(p+3)

Explanation:

`11.\ r^2 + 12r + 27\\Factorizing\\= r^2+9r+3r+27\\=r(r+9)+3(r+9)\\=(r+3)(r+9)\\\\12. g^2-9\\The\ expression\ will\ be\ factorized\ using\ the\ formula\\(a+b)(a-b)=a^2-b^2\\So,\\g^2-9\\=(g)^2-(3)^2\\=(g+3)(g-3)\\\\13. 2p^3 + 6p^2 + 3p + 9\\=2p^2(p+3)+3(p+3)\\=(2p^2+3)(p+3)` ..