How do you factor #2x^2+15x+18#?

3 Answers
Jun 16, 2016

Answer:

#(2x+3)(x+6)#

Explanation:

#2x^2+15x+18 = 2x^2+12x+3x+18 = 2x(x+6)+3(x+6)=(2x+3)(x+6)#[Ans]

Jun 16, 2016

#color(magenta)2x^2 + 15x color(lime)+ color(purple)18#

Find factors of #2 and 18# which ADD (because of #color(lime)(+)# 18) to make #15.#

The signs will be the same (because of the #color(lime)(+)18)#, they are both positive (because of the +15).

#2" "18#
#darr" "darr#

# color(red)(2)" "color(blue)(3) " cross multiply and ADD the products"#
# color(blue)(1)" "color(red)(6)#

# color(red)(2)" "color(blue)(3rArr 1 xx3 = 3)#
# color(blue)(1)" "color(red)(6 rArr 2 xx6 = ul12#
#color(white)(xxxxxxxx.xxxxx)15#

The top line gives one of the factors and the bottom line gives the other factor.

#(2x +3)(x + 6)#

Answer:

#(2x + 3)(x + 6)#

Explanation:

Use the new AC method (Socratic Search)

#y = 2x^2 + 15 x + 18 = 2(x + p)(x + q)#

Converted trinomial: #y' = x^2 + 15x + 36 = (x + p')(x + q').#

Find #p' and q'# knowing sum #(b = 15)# and product #(ac = 36).#

They are: #p' = 3 and q' = 12.#
Back to original #y rarr p = (p')/a = 3/2#, and #q = (q')/a = 12/2 = 6#.

Factored form: #2(x + 3/2)(x + 6) = (2x + 3)(x + 6)#