Final answer:
To divide (2x² - x - 10) by (x - 2), through long division, we find the quotient is 2x - 5 with a remainder of 0.Utilizing long division to divide (2x² - x - 10) by (x - 2), the quotient is determined as 2x - 5 with a remainder of 0. This result signifies that (2x² - x - 10) is evenly divisible by (x - 2), confirming the absence of a remainder and emphasizing the correctness of the division process.
Step-by-step explanation:
The student is asking for help with a long division of polynomials problem, specifically dividing (2x² - x - 10) by (x - 2) to find the quotient and the remainder using long division method. In the division of exponentials, it's important to divide the coefficients and subtract the exponents of like terms.
Let's perform the long division:
- Divide the leading term of the numerator by the leading term of the denominator, which gives us 2x.
- Multiply the entire denominator by 2x and subtract this from the original numerator.
- This leaves us with a new numerator of -5x - 10.
- Divide the leading term of this new numerator by the leading term of the denominator to get -5.
- Multiply the entire denominator by -5 and subtract this from the new numerator, which gives us the remainder.
The final quotient of the division is 2x - 5 and the remainder is 0.