Let's factor x2−25
x2−25
The middle number is 0 and the last number is -25.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get 0
Multiply together to get -25
Can you think of the two numbers?
Try 5 and -5:
5+-5 = 0
5*-5 = -25
Fill in the blanks in
(x+_)(x+_)
with 5 and -5 to get...
(x+5)(x-5)
Answer:
(x+5)(x−5)
<h2>
Hello!</h2>
The answer is: C) ![x^{3}+2x^{2}-3x-6](https://tex.z-dn.net/?f=x%5E%7B3%7D%2B2x%5E%7B2%7D-3x-6)
<h2>
Why?</h2>
Factoring we have:
![x^{3}+2x^{2}-3x-6=(x^{2})(x+2)-3(x+2)\\(x^{2})(x+2)-3(x+2)=(x+2)(x^{2}-3)\\(x+2)(x+\sqrt{3})(x-\sqrt{3})=0](https://tex.z-dn.net/?f=x%5E%7B3%7D%2B2x%5E%7B2%7D-3x-6%3D%28x%5E%7B2%7D%29%28x%2B2%29-3%28x%2B2%29%5C%5C%28x%5E%7B2%7D%29%28x%2B2%29-3%28x%2B2%29%3D%28x%2B2%29%28x%5E%7B2%7D-3%29%5C%5C%28x%2B2%29%28x%2B%5Csqrt%7B3%7D%29%28x-%5Csqrt%7B3%7D%29%3D0)
So,
![x_{1}=-2\\x_{2}=-\sqrt{3}\\x_{3}=\sqrt{3}](https://tex.z-dn.net/?f=x_%7B1%7D%3D-2%5C%5Cx_%7B2%7D%3D-%5Csqrt%7B3%7D%5C%5Cx_%7B3%7D%3D%5Csqrt%7B3%7D)
Let's substitute the roots into the equation,
Substituting: -2
![(-2+2)(x+\sqrt{3})(x-\sqrt{3})=(0)(x+\sqrt{3})(x-\sqrt{3})=0](https://tex.z-dn.net/?f=%28-2%2B2%29%28x%2B%5Csqrt%7B3%7D%29%28x-%5Csqrt%7B3%7D%29%3D%280%29%28x%2B%5Csqrt%7B3%7D%29%28x-%5Csqrt%7B3%7D%29%3D0)
Substituting: ![-\sqrt{3}](https://tex.z-dn.net/?f=-%5Csqrt%7B3%7D)
![(x+2)*(-\sqrt{3}+\sqrt{3})*(x-\sqrt{3})=(x+2)*(0)*(x-\sqrt{3})=0](https://tex.z-dn.net/?f=%28x%2B2%29%2A%28-%5Csqrt%7B3%7D%2B%5Csqrt%7B3%7D%29%2A%28x-%5Csqrt%7B3%7D%29%3D%28x%2B2%29%2A%280%29%2A%28x-%5Csqrt%7B3%7D%29%3D0)
Substituting: ![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
![(x+2)*(x+\sqrt{3})*(\sqrt{3}-\sqrt{3})=(x+2)*(x+\sqrt{3})*(0)=0](https://tex.z-dn.net/?f=%28x%2B2%29%2A%28x%2B%5Csqrt%7B3%7D%29%2A%28%5Csqrt%7B3%7D-%5Csqrt%7B3%7D%29%3D%28x%2B2%29%2A%28x%2B%5Csqrt%7B3%7D%29%2A%280%29%3D0)
Have a nice day!
Answer:
2 hours
Step-by-step explanation:
Circumference = pi × d
126 = 3.14 × d
d = 40.127388535 yards
d = 40 yards (nearest whole number)
Time = 40/20 = 2 hours
Answer:
Step-by-step explanation:
6 times, because 1/4 x 6/1= 3/2 which is equivalent to 1 1/2 :)