Amalia. Phones rule is only true with numbers between 1 and 1,000.
Answer:
b or 150
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
We can use the Polynomial Remainder Theorem. The PRT states that if we have a polynomial
being divided by a factor in the form of
, then the remainder of the polynomial is given by
.
We have the polynomial:
![f(x)=3x^{15}-5x^{12}+7x^6-3x^2+12](https://tex.z-dn.net/?f=f%28x%29%3D3x%5E%7B15%7D-5x%5E%7B12%7D%2B7x%5E6-3x%5E2%2B12)
And it is being divided by:
![(x+1)](https://tex.z-dn.net/?f=%28x%2B1%29)
We can rewrite our factor as:
![(x-(-1))](https://tex.z-dn.net/?f=%28x-%28-1%29%29)
Therefore:
![a=-1](https://tex.z-dn.net/?f=a%3D-1)
Then our remainder will be:
![f(-1)](https://tex.z-dn.net/?f=f%28-1%29)
Evaluate:
![\begin{aligned} f(-1)&=3(-1)^{15}-5(-1)^{12}+7(-1)^6-3(-1)^2+12\\&=-3-5+7-3+12\\&=8 \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20f%28-1%29%26%3D3%28-1%29%5E%7B15%7D-5%28-1%29%5E%7B12%7D%2B7%28-1%29%5E6-3%28-1%29%5E2%2B12%5C%5C%26%3D-3-5%2B7-3%2B12%5C%5C%26%3D8%20%5Cend%7Baligned%7D)
So, our remainder will be 8.
Answer:
D. Negative
Step-by-step explanation:
the line is facing down when looking at it left to right so it is negative.