Question

use long division to determine the remainder when 4x^3+9x-12 is divided by 2x+1
What restrictions must be placed on the value of x?
what do you think is the transformation of the graph on the parent function does the remainder cause?

Answer 1

I could answer just the first one. You could also use the remainder theorem. That is substitute the value of "c" of your divisor to the whole polynomial. Since your divisor is 2x+1, you should equate it to 0 to get the value of x.
2x+1=0
2x= -1
x= -1/2
Then substitute.
4(-1/2^3) + 9(-1/2)-12
4(-1/8) + -9/2 - 12
-1/2 + -9/2 -12
-10/ 2 -12
-5 - 12
-7
The remainder then is -7.