Answer :
The division of x⁴ - 10x³ by x - 2 will have a quotient of x³ - 8x² and a remainder of 16x² using synthetic division.
The procedure for synthetic division involves the following steps:
Divide.
Multiply.
Subtract.
Bring down the next term, and
Repeat the process to get zero or arrive at a remainder.
We shall divide x⁴ - 10x³ by x - 2 as follows;
x⁴ divided by x equals x³
x - 2 multiplied by x³ equals x⁴ - 2x³
subtract x⁴ - 2x³ from x⁴ - 10x³ will give -8x³
-8x³ divided by x equals -8x²
x - 2 multiplied by -8x² equals -8x³ - 16x²
subtract -8x³ - 16x² from -8x³ will give a remainder of 16x².
Therefore by synthetic division, x⁴ - 10x³ by divided by x - 2 will result to a quotient of x³ - 8x² and a remainder of 16x², so none of the options a to d is correct.
