The highlighted variables a = 6 , b = 2, c=6 , d =2 , e=6 , f =6 , g =1
<h3>What is an Expression ?</h3>
An expression is a mathematical statement which consists of variables , constants and mathematical operators.
![\rm \dfrac{2}{x^2-36}-\dfrac{1}{x^2+36}\\= \dfrac{2}{(x+6)(x-6)}-\dfrac{1}{x(x+a)}\\=\dfrac{bx}{x(x+6)(x-6)}-\dfrac{x-c}{x(x+6)(x-6)}\\\\=\dfrac{dx-x+e}{x(x+6)(x-6)}\\\\= \dfrac{x+f}{x(x+6)(x-6)}\\\\=\dfrac{g}{x(x-6)}](https://tex.z-dn.net/?f=%5Crm%20%5Cdfrac%7B2%7D%7Bx%5E2-36%7D-%5Cdfrac%7B1%7D%7Bx%5E2%2B36%7D%5C%5C%3D%20%5Cdfrac%7B2%7D%7B%28x%2B6%29%28x-6%29%7D-%5Cdfrac%7B1%7D%7Bx%28x%2Ba%29%7D%5C%5C%3D%5Cdfrac%7Bbx%7D%7Bx%28x%2B6%29%28x-6%29%7D-%5Cdfrac%7Bx-c%7D%7Bx%28x%2B6%29%28x-6%29%7D%5C%5C%5C%5C%3D%5Cdfrac%7Bdx-x%2Be%7D%7Bx%28x%2B6%29%28x-6%29%7D%5C%5C%5C%5C%3D%20%5Cdfrac%7Bx%2Bf%7D%7Bx%28x%2B6%29%28x-6%29%7D%5C%5C%5C%5C%3D%5Cdfrac%7Bg%7D%7Bx%28x-6%29%7D)
In the given expression
a = 6 , b = 2, c=6 , d =2 , e=6 , f =6 , g =1
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For this case we have the following polynomial:
![-24a ^ 6b ^ 4-40a ^ 3](https://tex.z-dn.net/?f=-24a%20%5E%206b%20%5E%204-40a%20%5E%203)
We must find the greatest common factor of the terms of the polynomial.
The GCF of the coefficients is given by:
![24 = 3 * 8\\40 = 5 * 8](https://tex.z-dn.net/?f=24%20%3D%203%20%2A%208%5C%5C40%20%3D%205%20%2A%208)
Then we look for the GFC of the variables:
We have then:
![a ^ 6 = a ^ 3a ^ 3\\a ^ 3 = a ^ 3](https://tex.z-dn.net/?f=a%20%5E%206%20%3D%20a%20%5E%203a%20%5E%203%5C%5Ca%20%5E%203%20%3D%20a%20%5E%203)
Finally rewriting we have:
![-24a ^ 6b ^ 4-40a ^ 3 = -8a ^ 3 (3a ^ 3b ^ 4 + 5)](https://tex.z-dn.net/?f=-24a%20%5E%206b%20%5E%204-40a%20%5E%203%20%3D%20-8a%20%5E%203%20%283a%20%5E%203b%20%5E%204%20%2B%205%29)
Answer:
the complete factored form of the polynomial is:
![-8a ^ 3 (3a ^ 3b ^ 4 + 5)](https://tex.z-dn.net/?f=-8a%20%5E%203%20%283a%20%5E%203b%20%5E%204%20%2B%205%29)
X + 2 = 10
X - 4 = 10
3x = 24
X/8 = 1
Those 4 are the correct answers
Answer:
16
Step-by-step explanation:
if ten dove int the water and 6 came back up there would be 4 left in the water.If there are now 12 penguins on the ice then there were 16 penguins to begin with.