Answer:
9
Step-by-step explanation:
First you put in b, which would look like this: 4(1/4+2)
Then you could do it two ways, you can use distributive property, or just add within the parenthisis.
Distributive Property:
it would be 4* 1/4, which is one, and add 4*2, which is nine.
Parenthesis:
just add 2 and 1/4, which is 2 1/4. 2 1/4 is equal to 9/4, and that times 4 is nine.
Hope it helps!
Answer:
-17/9
Step-by-step explanation:
You need to add 7 to both sides.
-9x - 7 = 10
-9x -7 + (7) = 10 + 7
-9x = 17
Then both sides for (-9)
-9x/(-9) = 17/(-9)
x = -17/9
By either long or synthetic division, it's easy to show that
![\dfrac{x^4+ax^3+bx^2+cx+d}{x+1}=x^3+(a-1)x^2+(-a+b+1)x+(a-b+c-1)-\dfrac{a-b+c-d-1}{x+1}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E4%2Bax%5E3%2Bbx%5E2%2Bcx%2Bd%7D%7Bx%2B1%7D%3Dx%5E3%2B%28a-1%29x%5E2%2B%28-a%2Bb%2B1%29x%2B%28a-b%2Bc-1%29-%5Cdfrac%7Ba-b%2Bc-d-1%7D%7Bx%2B1%7D)
The quartic will be exactly divisible by
![x+1](https://tex.z-dn.net/?f=x%2B1)
when the numerator of the remainder term vanishes, or for those values of
![a,b,c,d](https://tex.z-dn.net/?f=a%2Cb%2Cc%2Cd)
such that
![a-b+c-d-1=0](https://tex.z-dn.net/?f=a-b%2Bc-d-1%3D0)
I'm not sure how to count the number of solutions (software tells me it should be 80), but hopefully this is a helpful push in the right direction.