Question

6g^2 +17gd +12d^2
factor completely and simplify

Answer 1

(2g+3d)(3g+4d) factored

Answer 2

thank you!

Answer 3

:) thats simplyed already

Answer 4

6g^2+17gd+12d^2
6g^2+17dg+12d^2
Ag^2+Bg+C
so A=6, B=17d, C=12d^2

The trick is to find two factors of A*C that multiply to be A*C and add up to be B.

A*C=(6)*(12d^2)=6d*12d=18d*4d=9d*8d
and
B=17d=8d+9d

so replace Bg=17dg with 8dg+9dg

so we have
6g^2+8dg+9dg+12d^2
now we factor by grouping

(6g^2+8dg)+(9dg+12d^2)

in the first paranthesis what do 6g^2 and 8dg have in common
they have 2g in common so we can factor 2g out of first paranthesis
so we have
2g(3g+4d)+(9dg+12d^2)

now what do 9dg and 12d^2 have in common
they have 3d in common so factor that out in the second paranthesis

so we have
2g(3g+4d)+3d(3g+4d)

so since we have 3g+4d in both terms we can factor that our

(3g+4d)(2g+3d)