Answer:
c=2
The remainder is 7.
Step-by-step explanation:
They want you to subtract those last two lines:
[tex]0x^4+0x^3-5x^2-18x[/tex]
[tex]-(0x^4+0x^3-5x^2-20x)[/tex]
----------------------------------------------------
[tex]0x^4+0x^3+0x^2+2x[/tex].
2x comes from doing -18-(-20) or -18+20.
Then you bring down the +15 so you have 2x+15 below that last bar in the picture.
Anyways, you then need to find how many times x goes into 2x or what times x gives you 2x?
Hopefully you say 2 here and put that as c.
Now anything you put above the bar has to be multiplied to your divisor so 2(x+4)=2x+8.
We want to see what's left over from subtract (2x+15) and (2x+8). That gives you a remainder of 15-8=7.
Here are my steps for this division:
4x^3+2x^2-5x+2
-------------------------------------
x+4| 4x^4+18x^3+3x^2-18x+15
-(4x^4+16x^3)
--------------------------------------
2x^3+3x^2-18x+15
-(2x^3+8x^2)
----------------------------
-5x^2-18x+15
-( -5x^2-20x)
----------------------------
2x+15
-( 2x+8)
------------
7
c=2
The remainder is 7.
