Question

Solve the following polynomial division:

\[(3x^{2} - 4x + 2) \div (x + 3)\]

A) \(3x - 5\)

B) \(3x - 5 + \frac{41}{x + 3}\)

C) \(x - 5\)

D) \(3x + 5 - \frac{41}{x + 3}\)

Answer 1

To divide the polynomial 3x^2 - 4x + 2 by x + 3, use long division to find the quotient and remainder. The correct answer is option A) 3x - 5.

Step-by-step explanation:

To divide the polynomial 3x^2 - 4x + 2 by x + 3, we can use long division.

First, divide the leading term of the polynomial by the leading term of the divisor: 3x^2 / x = 3x.

Next, multiply the divisor x + 3 by the quotient 3x to get 3x^2 + 9x.

Subtract this from the original polynomial to get the remainder: (3x^2 - 4x + 2) - (3x^2 + 9x) = -13x + 2.

The final result is 3x - 5 with a remainder of -13x + 2. Therefore, the correct answer is option A) 3x - 5.