Answer: quotient = 2x³ - x² + 3x - 11
Remainder = 25
Explanation:
The given polynomial function is expressed as
f(x) = 2x⁴ + 5x³ - 2x - 8
We want to divide by (x + 3). Let us determine the remainder by substituting x = - 3 into the given polynomial. It becomes
2(- 3)⁴ + 5(- 3)³ - 2(- 3) - 8
= 25
The long division method will give us the quotient and the remainder.
The steps are shown in the attached photo. Firstly, the first term of the polynomial is divided by the divisor. The quotient is used to multiply each term in the divisor and the resulting polynomial is subtracted or added(depending on whether they are like terms in terms of signs or not) to the previous polynomial. The same step is carried out on the new polynomial until it cannot be divided further. The quotient is 2x³ - x² + 3x - 11 while the remainder is 25