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Simplify the expression (x3 - 4x2 + 9x - 10) + (x - 2) using long division.

A. (x2 - 3x + 5)
B. (x2 - 5x + 7)
C. (x2 - 2x + 9)
D. (x2 - 6x + 12)

1 Answer

1 vote

Final answer:

The expression (x^3 - 4x^2 + 9x - 10) + (x - 2) simplifies to x^3 - 4x^2 + 10x - 12 by combining like terms, which does not require long division.

Step-by-step explanation:

To simplify the expression (x3 - 4x2 + 9x - 10) + (x - 2) we start by combining like terms. In this case, the expression does not require long division; instead, we simply add the corresponding coefficients of the same powers of x.

Combining like terms, we get:

  • x3 from the first polynomial;
  • -4x2 (there is no x2 term in the second polynomial);
  • (9x + x) which simplifies to 10x;
  • (-10 - 2) which simplifies to -12.

Thus, the simplified form of the given expression is x3 - 4x2 + 10x - 12, which does not match any of the options given (A through D). Either the question or the options provided may contain a mistake, or we may require additional instructions such as further simplification after dividing the result by another expression if long division is indeed necessary.

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