Question

If 2x³ −9x² +4x−7 is divided by x−3 to give a quotient of 2x² −3x−5 and a remainder of −22, then which of the following is true?

A. 2x³ −9x² +4x−7=(x−3)(2x² −3x−5)+22
B. (x−3)(2x² −3x−5)=22
C. 2x³ −9x² +4x−7=(2x² −3x−5)(x−3)−22
D. (2x³ −9x² +4x−7)−22=(x−3)(2x² −3x−5)
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Answer 1

The correct statement is A, which indicates the original polynomial equals the product of its divisor and quotient plus the given remainder.

Step-by-step explanation:

The correct statement regarding the division of the given polynomial 2x³ −9x² +4x−7 by x−3 with a quotient of 2x² −3x−5 and a remainder of −22 is:

A. 2x³ −9x² +4x−7=(x−3)(2x² −3x−5)+22

When a polynomial is divided by a binomial of the form (x − a), the result is a quotient and a possible remainder. In this case, we must add the remainder to the product of the divisor and the quotient to represent the original polynomial correctly. Therefore, the given polynomial equals the product of its divisor and quotient plus the remainder.