Answer:
f(x)/g(x) = x - 6 + (2x+3)/(2x^2+5)
Quotient = x - 6
Remainder = (2x+3)/(2x^2+5)
Step-by-step explanation:
Getting x-6:
What number multiplies with 2x²+5 to get 2x³+...?
that number is x, so that's your first number. You multiply it with 2x²+5 and subtract it like how you would do divison by hand back in elementary school.
Now what number multiplies with 2x²+5 to get -12x²+ ...?
that number would be 6, so that's your second number. Multiply 2x²+5 with 6 and subtract it from -12x²+ ....
Now you have 2x+3. What number multiplies with 2x²+5 to get 2x+3? That number doesnt exist so 2x+3 is your remainder.
