Question

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

a) x² - 2x - 5
b) x² - 2x + 5
c) x² + 2x - 5
d) x² + 2x + 5

Answer 1

The simplification of the expression (x³ - 4x² + 9x - 10) ÷ (x - 2) using long division results in x² - 2x + 5, which is option b) from the given choices.

Step-by-step explanation:

To simplify the expression using long division: (x³ - 4x² + 9x - 10) ÷ (x - 2), follow these steps:

1. Divide the first term of the numerator by the first term of the denominator: x³ ÷ x = x².
2. Multiply the entire denominator by this quotient: (x - 2)(x²) = x³ - 2x².
3. Subtract the result from the original polynomial:
   (x³ - 4x² + 9x - 10) - (x³ - 2x²) = -2x² + 9x - 10.
4. Repeat these steps until the degree of the remainder is less than the degree of the denominator.

The result of the division is x² - 2x + 5, which corresponds to option b) from the multiple choices provided in the question.