Answer:
a
Step-by-step explanation:
go it right on a mastery test
Answer:
See Below.
Step-by-step explanation:
By the Factor Theorem, if we divide <em>q(x)</em> into <em>p(x) </em>and the resulting remainder is 0, then <em>p(x)</em> is divisible by <em>q(x)</em> (i.e. there are no remainders).
Problem 1)
We are given:
![p(x)=x^3+3x^2+3x+1\text{ and } q(x)=x+1](https://tex.z-dn.net/?f=p%28x%29%3Dx%5E3%2B3x%5E2%2B3x%2B1%5Ctext%7B%20and%20%7D%20q%28x%29%3Dx%2B1)
We should find the remainder when dividing <em>p(x)</em> and <em>q(x)</em>. We can use the Polynomial Remainder Theorem. When dividing a polynomial <em>p(x)</em> by a binomial in the form of (<em>x</em> - <em>a</em>), then the remainder will be <em>p(a).</em>
Here, our divisor is (<em>x</em> + 1) or (<em>x</em> - (-1)). So, <em>a </em>= -1.
Then by the Polynomial Remainder Theorem, the remainder when performing <em>p(x)/q(x)</em> is:
![p(-1)=(-1)^3+3(-1)^2+3(-1)+1=0](https://tex.z-dn.net/?f=p%28-1%29%3D%28-1%29%5E3%2B3%28-1%29%5E2%2B3%28-1%29%2B1%3D0)
The remainder is 0, satisfying the Factor Theorem. <em>p(x)</em> is indeed divisible by <em>q(x)</em>.
Problem 2)
We are given:
![p(x)=x^3-2x^2+6x-27\text{ and } q(x)=x-3](https://tex.z-dn.net/?f=p%28x%29%3Dx%5E3-2x%5E2%2B6x-27%5Ctext%7B%20and%20%7D%20q%28x%29%3Dx-3)
Again, use the PRT. In this case, <em>a</em> = 3. So:
![p(3)=(3)^3-2(3)^2+6(3)-27=0](https://tex.z-dn.net/?f=p%283%29%3D%283%29%5E3-2%283%29%5E2%2B6%283%29-27%3D0)
It satisfies the Factor Theorem.
Problem 3)
We are given:
![p(x)=x^n-10^n\text{ and } q(x)=x-10](https://tex.z-dn.net/?f=p%28x%29%3Dx%5En-10%5En%5Ctext%7B%20and%20%7D%20q%28x%29%3Dx-10)
Use the PRT. In this case, <em>a</em> = 10. So:
![p(10)=(10)^n-10^n=0](https://tex.z-dn.net/?f=p%2810%29%3D%2810%29%5En-10%5En%3D0)
It satisfies the Factor Theorem.
Since all three cases satisfy the Factor Theorem, <em>p(x)</em> is divisible by <em>q(x)</em> in all three instances.
Answer:
x=6t+9 y=-8-1
Step-by-step explanation:
Answer:
Option A & D are correct Option.
Step-by-step explanation:
We are given with following :
Area of Base = 15 in.²
Height of Prism = 3 in.
Length of edge of base = 5 in.
Volume of Prism = Area of Base × Height = 15 × 3 = 45 in.³
Therefore, Option A & D are correct Option.