The question "how much greater is #a# than #b#?" can be expressed mathematically as:

#a-b=D#

where #D# is the difference between #a# and #b#.

The problem then is to evaluate #D# in the expression:

#(-12x^2-19x+8)-(-15x^2+17x-18)=D#

First distribute the minus sign to every term in the parentheses.

#rArr-12x^2-19x+8-(-15x^2)-(17x)-(-18)=D#

#rArr-12x^2-19x+8+15x^2-17x+18=D#

Now group similar terms.

#rArr(-12x^2+15x^2)+(-19x-17x)+(8+18)=D#

#rArr(-12+15)x^2+(-19-17)x+(8+18)=D#

#rArr3x^2-36x+26=D#

This is our answer. If we were to substitute any value of #x# into the two given polynomials, the difference between them would be #color(red)(3x^2-36x+26)#.

Let's check our answer to prove that it is correct.

Substitute #x=0#

#-12(0)^2-19(0)+8 = 8#

#-15(0)^2+17(0)-18 = -18#

The difference between them is

#8-(-18)=color(blue)26#

and our solution gives

#3(0)^2-36(0)+26 = color(blue)26#