Final answer:
To divide the expression 3x³+2x+5 by x+2, perform long division. The quotient is 3x²-4x+10 with a remainder of -18x²+2x+5.
Step-by-step explanation:
To divide the expression 3x³+2x+5 by x+2, we can use long division. The first step is to divide 3x³ by x, which gives us 3x². Then, we multiply (x+2) by 3x² to get 3x³+6x². Subtracting this from the original expression gives us -4x²+2x+5. Now, we divide -4x² by x, which gives us -4x. Multiplying (x+2) by -4x gives us -4x³-8x². Subtracting this from the previous step gives us 10x²+2x+5. Finally, we divide 10x² by x, which gives us 10x. Multiplying (x+2) by 10x gives us 10x³+20x². Subtracting this from the previous step gives us -18x²+2x+5. So, the quotient is 3x²-4x+10 with a remainder of -18x²+2x+5.