Answer:
Let's solve for a.
(ax2+bx+3)(x+d)=x3+6x2+11x+12a+2b−d
Step 1: Add -12a to both sides.
adx2+ax3+bdx+bx2+3d+3x+−12a=x3+6x2+12a+2b−d+11x+−12a
adx2+ax3+bdx+bx2−12a+3d+3x=x3+6x2+2b−d+11x
Step 2: Add -bdx to both sides.
adx2+ax3+bdx+bx2−12a+3d+3x+−bdx=x3+6x2+2b−d+11x+−bdx
adx2+ax3+bx2−12a+3d+3x=−bdx+x3+6x2+2b−d+11x
Step 3: Add -bx^2 to both sides.
adx2+ax3+bx2−12a+3d+3x+−bx2=−bdx+x3+6x2+2b−d+11x+−bx2
adx2+ax3−12a+3d+3x=−bdx−bx2+x3+6x2+2b−d+11x
Step 4: Add -3d to both sides.
adx2+ax3−12a+3d+3x+−3d=−bdx−bx2+x3+6x2+2b−d+11x+−3d
adx2+ax3−12a+3x=−bdx−bx2+x3+6x2+2b−4d+11x
Step 5: Add -3x to both sides.
adx2+ax3−12a+3x+−3x=−bdx−bx2+x3+6x2+2b−4d+11x+−3x
adx2+ax3−12a=−bdx−bx2+x3+6x2+2b−4d+8x
Step 6: Factor out variable a.
a(dx2+x3−12)=−bdx−bx2+x3+6x2+2b−4d+8x
Step 7: Divide both sides by dx^2+x^3-12.
a(dx2+x3−12)
dx2+x3−12
=
−bdx−bx2+x3+6x2+2b−4d+8x
dx2+x3−12
a=
−bdx−bx2+x3+6x2+2b−4d+8x
dx2+x3−12
Answer:
a=
−bdx−bx2+x3+6x2+2b−4d+8x/
dx2+x3−12
Explanation: