Final answer:
To find the trinomial that represents C when A=3x²+5x-6 and B=-2x²-6x+7, substitute the given values of A and B into the equation C=A-2B.
Step-by-step explanation:
To find the trinomial that represents C when A=3x²+5x-6 and B=-2x²-6x+7, we substitute the given values of A and B into the equation C=A-2B. First, we distribute the -2 to each term in B to get -2B=(-2)(-2x²)+(-2)(-6x)+(2)(7)=4x²+12x-14. Then, we substitute the values of A and -2B into the equation C=A-2B to find the trinomial:
C=(3x²+5x-6)-(4x²+12x-14) = 3x²+5x-6-4x²-12x+14 = -x²-7x+8.