Question

Given P(x)= x - 4x² - 2x +6,
find the quotient of P(x) and x + 2
by long division.

Answer 1

To find the quotient of P(x) and x + 2 by long division, divide the first term of P(x) by the first term of x + 2, then multiply and subtract iteratively. Carry down terms until the division is complete.

Step-by-step explanation:

The student is asking to find the quotient of the polynomial P(x) = x - 4x² - 2x + 6 when divided by x + 2 using long division. To do this, we'll follow the long division process step by step:

1. Divide the first term of the numerator (x) by the first term of the denominator (x) to get -4x. Place this above the long division bar.
2. Multiply the entire denominator by -4x and subtract the result from the polynomial P(x).
3. Bring down the next term (-2x), and repeat the process until all terms have been brought down and the remainder, if any, is less than the degree of the denominator.
4. Record the quotient and remainder (if any).

Upon completion of this process, we will have the answer to the division problem. The key is to carefully align like terms, subtract accurately, and bring down the next terms in sequence.