With the information provided we can write:
#6x^2 + 19x + c = (2x + 5)(ax + b)#
Cross multiplying the terms on the right of the equation gives:
#6x^2 + 19x + c = 2ax^2 + 5ax + 2bx + 5b#
#6x^2 + 19x + c = 2ax^2 + (5a + 2b)x + 5b#
Therefore we know:
#6x^2 = 2ax^2# Solving for #a# gives.
#(6x^2)/x^2 = (2ax^2)/x^2#
#6 = 2a#
#(2a)/2 = 6/2#
#a = 3#
Substituting this back into the equation gives:
#6x^2 + 19x + c = 2*3x^2 + (5*3 + 2b)x + 5b#
#6x^2 + 19x + c = 6x^2 + (15 + 2b)x + 5b#
Therefore we know:
#19x = (15 + 2b)x# Solving for #b# gives:
#(19x)/x = ((15 + 2b)x)/x#
#19 = 15 + 2b#
#19 - 15 = 15 - 15 + 2b#
#4 = 2b#
#(2b)/2 = 4/2#
#b = 2#
Substituting this back into the equation gives:
#6x^2 + 19x + c = 6x^2 + (15 + 2*2)x + 5*2#
#6x^2 + 19x + c = 6x^2 + (15 + 4)x + 10#
#6x^2 + 19x + c = 6x^2 + 19x + 10#
Therefore #c = 10#
