The polynomial which when divided by −x² + x − 1 gives quotient x − 2 and remainder 3

Video Explanation

Watch the video explanation below:

Given

Divisor = −x² + x − 1

Quotient = x − 2

Remainder = 3

To Find

The dividend polynomial.

Solution

By the Division Algorithm:

Dividend = (Divisor × Quotient) + Remainder

Step 1: Substitute the Given Values

Dividend = (−x² + x − 1)(x − 2) + 3

Step 2: Multiply

(−x² + x − 1)(x − 2)

= −x³ + 2x² + x² − 2x − x + 2

= −x³ + 3x² − 3x + 2

Step 3: Add the Remainder

Dividend = −x³ + 3x² − 3x + 2 + 3

= −x³ + 3x² − 3x + 5

Final Answer

The required polynomial is:

−x³ + 3x² − 3x + 5

Correct Option

(c) −x³ + 3x² − 3x + 5

Conclusion

Hence, the polynomial which when divided by −x² + x − 1 gives quotient x − 2 and remainder 3 is −x³ + 3x² − 3x + 5.