How do you factor #54 + 27t + 3t^2#?

Question

1568 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-28T00:17:35

#f(t) = 3(t^2 + 9t + 18) = 3(t - p)(t - q)#

Find p and q by composing factor pairs of #18#: #(1, 18);(2, 9);(3, 6)#.

#p = 3# and #q = 6#.

#f(x) = 3[(t + 3)(t + 6)]#

Answer 2 · 2015-05-28T03:46:25

Answer: #3t^2+27t+54=3(t+3)(t+6)#

Problem: Factor #54+27t+3t^2#.

Rewrite the equation as #3t^2+27t+54#.

Factor out the GCF #3#.

#3(t^2+9t+18)#

Factor #(t^2+9t+18)# by determining two factors of #18# that when added equal #9#.

The numbers #3# and #6# meet the requirement.

The factors for #3t^2+27t+54# are #3(t+3)(t+6)#.