Answer:
(d) x² -2x +3
Explanation:
You want the quotient (x³ - 3x² + 5x - 3) ÷ (x - 1).
Quick Check
The constant in a product will be the product of the constants in the factors. That is if (x² +bx +c) is a factor of the cubic, we must have ...
-1·c = -3 . . . . . . . where the other factor is (x -1), having constant -1
c = 3
Only one answer choice matches: x²-2x+3.
Synthetic division
Using synthetic division to find the entire quotient can be almost as fast.
The tableau is shown in the attachment. It tells you the quotient is ...
x² -2x +3
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Additional comment
"The entry in the left part of the table" is the zero of the binomial divisor. The divisor (x-1) is zero when x=1, so that entry is 1.
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