Answer:
I only used two steps: 3) then 6) then 1).
Step-by-step explanation:
Ok, if x-5 is a factor of p(x), then p(5)=0 by factor theorem.
This also goes the other way around:
If p(5)=0 then x-5 is a factor of p(x) by factor theorem.
Let's check. I'm going to evaluate p(x) for x=5.
![p(5)=5^3-5(5)^2-5+5](https://tex.z-dn.net/?f=p%285%29%3D5%5E3-5%285%29%5E2-5%2B5)
![p(5)=125-5(25)-5+5](https://tex.z-dn.net/?f=p%285%29%3D125-5%2825%29-5%2B5)
![p(5)=125-125-5+5](https://tex.z-dn.net/?f=p%285%29%3D125-125-5%2B5)
![p(5)=0+0](https://tex.z-dn.net/?f=p%285%29%3D0%2B0)
![p(5)=0](https://tex.z-dn.net/?f=p%285%29%3D0)
This implies x-5 is a factor since we have p(5)=0.
The first step I did was 3) evaluate p(x) for x=5.
The second step I did 6) simplify and find the remainder. I did this when I was evaluating p(5); that was a lot of simplification and then I found the remainder to be 0 after that simplification. The last step was 1) apply the factor theorem, the remainder is 0 so x-5 is a factor of p(x).
Answer:
t=4h
Steps below
Step-by-step explanation:
We know:
speed of boat with respect to earth: 13 km
speed of stream with respect to earth: 4 km
13 km/h + 4 km/h = 17 km/h The time to travel 68 km with this speed is thus t = 68 km 17 km h = 4 h
<em><u>Hope this helps.</u></em>
Answer: ooh. That's a nice shape!
Step-by-step explanation:
Answer:
Find a common denominator on the right side of the equation.
Step-by-step explanation:
On the right side of the equation we began with
![-\frac{c}{a} +\frac{b^2}{4a^2}](https://tex.z-dn.net/?f=-%5Cfrac%7Bc%7D%7Ba%7D%20%2B%5Cfrac%7Bb%5E2%7D%7B4a%5E2%7D)
Then we ended with
![-\frac{4ac}{4a^2} +\frac{b^2}{4a^2}](https://tex.z-dn.net/?f=-%5Cfrac%7B4ac%7D%7B4a%5E2%7D%20%2B%5Cfrac%7Bb%5E2%7D%7B4a%5E2%7D)
As we can see, only the left term changed. It was multiplied by
. This was done in order to match the denominator of the right term.
As you can see they now match.