Question 6 Find the quotient and remainder using long division for: $\frac{2 x^{3}-16 x^{2}+7 x-38}{2 x^{2}+5}$ The quotient is The remainder is Question Help: Video Submit Question

Step 1 ：We are asked to find the quotient and remainder when the polynomial \(2 x^{3}-16 x^{2}+7 x-38\) is divided by \(2 x^{2}+5\). This is a polynomial division problem.

Step 2 ：The process of polynomial division is similar to the process of numerical long division. We divide the highest degree term of the dividend by the highest degree term of the divisor to find the first term of the quotient. Then we multiply the divisor by this term and subtract the result from the dividend to find the remainder. We repeat this process until the degree of the remainder is less than the degree of the divisor.

Step 3 ：Let's denote the variable as \(x\). The dividend is \(2x^{3} - 16x^{2} + 7x - 38\) and the divisor is \(2x^{2} + 5\).

Step 4 ：By performing the division, we can find the quotient and the remainder.

Step 5 ：The quotient and remainder of the division \(\frac{2 x^{3}-16 x^{2}+7 x-38}{2 x^{2}+5}\) are given by the output of the calculation.