Questions: Divide. [ left(4 s^4+3 s^3-9 s^2-3 s+12right) divleft(s^2-2right) ] Choose the correct answer. A. 4 s^2+3 s+1, R 3 s B. 4 s^2+3 s-1 C. 4 s^2-3 s-1, R 10 D. 4 s^2+3 s-1, R 3 s+10

Solution Steps

To solve the polynomial division problem, we can use polynomial long division or synthetic division. Here, we will use polynomial long division to divide \(4s^4 + 3s^3 - 9s^2 - 3s + 12\) by \(s^2 - 2\). We will find the quotient and the remainder.

We are tasked with dividing the polynomial \(4s^4 + 3s^3 - 9s^2 - 3s + 12\) by \(s^2 - 2\). Using polynomial long division, we find the quotient and remainder.

The division yields:

• Quotient: \(4s^2 + 3s - 1\)
• Remainder: \(3s + 10\)

This can be expressed mathematically as: \[ \frac{4s^4 + 3s^3 - 9s^2 - 3s + 12}{s^2 - 2} = 4s^2 + 3s - 1 + \frac{3s + 10}{s^2 - 2} \]

Final Answer