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If a polynomial is divided by \( x-8 \), the quotient is \( 2x^2+3x-5 \) and the remainder is 8. Find the original polynomial.

A. \( 2x^3+3x^2-5x+8 \)

B. \( 2x^3+11x^2-5x+8 \)

C. \( 2x^3+3x^2-5x+48 \)

D. \( 2x^3+11x^2-5x+48 \)

Answer :

Final answer:

The original polynomial when a polynomial is divided by (x-8) giving quotient as 2x2+3x-5 and remainder as 8, should be 2x3-13x2 -29x + 48 according to the polynomial division rule, which is not given in the provided options. Hence, there might be a mistake in the question or options.

This correct answer is none of above.

Explanation:

In Mathematics, specifically in algebra, when a polynomial is divided by another polynomial, the dividend can be represented as the divisor times the quotient plus the remainder.

So, if a polynomial is divided by (x-8), and the quotient is 2x2+3x-5 and the remainder is 8, the original polynomial can be represented as (x-8)*(2x2+3x-5) + 8.

Expanding the brackets, we get 2x3-16x2 +3x2 -24x -5x +40 +8. By combining like terms, it equals to 2x3-13x2 -29x + 48. From the options given, none of them matches with the result.

So, there might been a typographical error in the provided options or the question itself.

This correct answer is none of above.

Learn more about Polynomial Division here:

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