The process of synthetic division is somewhat like long division.
First choose a multiplier for (x+4)(x+4) that will result in an expression whose highest order term matches the highest order term of (6x^2+7x-2)(6x2+7x−2).
That multiplier is 6x6x...
6x*(x+4) = 6x^2+24x6x⋅(x+4)=6x2+24x
Subtract this from the original value to leave a remainder...
(6x^2+7x-2) - (6x^2+24x)(6x2+7x−2)−(6x2+24x)
=6x^2+7x-2-6x^2-24x=6x2+7x−2−6x2−24x
=-17x-2=−17x−2
Now choose a multiplier for (x+4)(x+4) that will result in an expression whose highest order term matches the highest order term of (-17x-2)(−17x−2)
That multiplier is -17−17
-17(x+4) = -17x-68−17(x+4)=−17x−68
Subtract this from the previous remainder to get a new remainder:
(-17x-2)-(-17x-68)(−17x−2)−(−17x−68)
=-17x-2+17x+68=−17x−2+17x+68
=66=66
So
(6x^2+7x-2) = (x+4)(6x-17)+66(6x2+7x−2)=(x+4)(6x−17)+66
or
(6x^2+7x-2)/(x+4) = (6x-17)+66/(x+4)6x2+7x−2x+4=(6x−17)+66x+4
