How do you factor #5x^2+27x+36#?

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Answer 1 · 2016-08-14T13:03:41

#(5x+12)(x+3)#

Read all the clues and information from the signs and numbers.

#color(green)(5)x^2color(blue)(+)color(magenta)(27)xcolor(red)+color(green)(36)#

Find factors of #color(green)(5 and 36 )# which #color(red)(ADD )# to give # color(magenta)( 27).#

The signs are #color(red)("the SAME")# , they are #color(blue)"both positive"#

Choose factors and find the cross-products.
A bit of trial and error will result in the following.

#color(white)(.......) 5" "12 rArr 1xx 12 = 12#
#color(white)(.......) 1" "3 rArr 5 xx3 + 15" "12+15 = 27#

The top row is the first bracket, the second row is the second row.

#(5x+12)(x+3)#