Question

Divide using long division. (5x²-2x+6)-:(x-1)

Answer 1

To divide the expression (5x²-2x+6) by (x-1) using long division, follow the steps: arrange terms, divide, multiply, subtract, repeat until all terms have been divided. The result is 5x + 3 with a remainder of (-3x + 6)/(x-1).

Step-by-step explanation:

To divide the expression (5x²-2x+6) by (x-1) using long division, follow these steps:

1. Arrange the terms in decreasing order of their exponent: 5x² - 2x + 6
2. Divide the first term of the dividend (5x²) by the first term of the divisor (x) to get the quotient term, which is 5x.
3. Multiply the divisor (x-1) by the quotient term (5x) to get the product (5x² - 5x).
4. Subtract the product (5x² - 5x) from the dividend (5x² - 2x + 6) to get the remainder (-3x + 6).
5. Bring down the next term (-3x) and repeat the steps until all terms have been divided.

Therefore, the division of (5x²-2x+6) by (x-1) using long division is 5x + 3 with a remainder of (-3x + 6)/(x-1).

Answer 2

To divide (5x² - 2x + 6) by (x - 1) using long division, we can follow these steps:

5x - 3

____________

x - 1|5x² - 2x + 6

- (5x² - 5x)

------------

3x + 6

- (3x - 3)

--------

9

Therefore, the quotient is 5x - 3 and the remainder is 9.

We can write the division as:

5x² - 2x + 6 = (x - 1)(5x - 3) + 9