The evaluation of the algebraic fraction x+2x+1/x^2-25 is![\mathbf{\implies -\dfrac{3}{5(x+5)} +\dfrac{18}{5(x-5)}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cimplies%20-%5Cdfrac%7B3%7D%7B5%28x%2B5%29%7D%20%2B%5Cdfrac%7B18%7D%7B5%28x-5%29%7D%7D)
<h3>What is the division of algebraic expression?</h3>
The division of an algebraic expression can be carried out by using the long division method or expansion of the.
Given that:
![\mathbf{\dfrac{x+2x+21}{x^2-25}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cdfrac%7Bx%2B2x%2B21%7D%7Bx%5E2-25%7D%7D)
where:
By expanding the denominator, we have:
![\mathbf{\dfrac{x+2x+21}{(x+5)(x-5)}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cdfrac%7Bx%2B2x%2B21%7D%7B%28x%2B5%29%28x-5%29%7D%7D)
![\mathbf{\dfrac{3x+21}{(x+5)(x-5)}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cdfrac%7B3x%2B21%7D%7B%28x%2B5%29%28x-5%29%7D%7D)
Creating a partial fraction from the denominator, we have:
![\mathbf{\dfrac{3x+21}{(x+5)(x-5)} = \dfrac{a_o}{x+5} +\dfrac{a_1}{x-5}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cdfrac%7B3x%2B21%7D%7B%28x%2B5%29%28x-5%29%7D%20%3D%20%5Cdfrac%7Ba_o%7D%7Bx%2B5%7D%20%2B%5Cdfrac%7Ba_1%7D%7Bx-5%7D%7D)
Multiply the equation by the denominator, and we have:
![\mathbf{\dfrac{(3x+21)(x+5)+(x-5)}{(x+5)(x-5)} = \dfrac{a_o(x+5)(x-5)}{x+5} +\dfrac{a_1(x+5)(x-5)}{x-5}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cdfrac%7B%283x%2B21%29%28x%2B5%29%2B%28x-5%29%7D%7B%28x%2B5%29%28x-5%29%7D%20%3D%20%5Cdfrac%7Ba_o%28x%2B5%29%28x-5%29%7D%7Bx%2B5%7D%20%2B%5Cdfrac%7Ba_1%28x%2B5%29%28x-5%29%7D%7Bx-5%7D%7D)
Simplifying, we have:
3x + 21 = a₀(x-5)+a₁(x+5)
Solve for the unknown parameter by plugging the real roots of the denominator: -5, 5
![\mathbf{a_o =\dfrac{-3}{5}}](https://tex.z-dn.net/?f=%5Cmathbf%7Ba_o%20%3D%5Cdfrac%7B-3%7D%7B5%7D%7D)
![\mathbf{a_1 =\dfrac{18}{5}}](https://tex.z-dn.net/?f=%5Cmathbf%7Ba_1%20%3D%5Cdfrac%7B18%7D%7B5%7D%7D)
Replacing the solutions into the partial fractions parameters to obtain the final result, we have:
![\mathbf{\dfrac{-(\dfrac{3}{5})}{x+5} +\dfrac{\dfrac{18}{5}}{x-5}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cdfrac%7B-%28%5Cdfrac%7B3%7D%7B5%7D%29%7D%7Bx%2B5%7D%20%2B%5Cdfrac%7B%5Cdfrac%7B18%7D%7B5%7D%7D%7Bx-5%7D%7D)
![\mathbf{\implies -\dfrac{3}{5(x+5)} +\dfrac{18}{5(x-5)}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cimplies%20-%5Cdfrac%7B3%7D%7B5%28x%2B5%29%7D%20%2B%5Cdfrac%7B18%7D%7B5%28x-5%29%7D%7D)
Learn more about the division of algebraic fractions here:
brainly.com/question/24705296
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All of them
the roots of thhe equaiton are the x intercept
they would be at x=5 and x=-2
<u>Answer:</u>
The polynomial is
.
<u>Explanation:</u>
Given:
Real zeros: -3,0,2
Degree 3
To Find:
The polynomial
Solution:
Now, according to given information, x = -3, x = 0 and x = 2 are zeros of equation.
Then, x – (-3) x + 3, x and x – 2 are the factors of the equation.
Now, multiply the factors, such that we will get equation.
x(x + 3)(x – 2)
![x(x^2 + 3-2x- 6)](https://tex.z-dn.net/?f=x%28x%5E2%20%2B%203-2x-%206%29)
![x(x^2+ x-6)](https://tex.z-dn.net/?f=x%28x%5E2%2B%20x-6%29)
![x^3 + x^2-6x](https://tex.z-dn.net/?f=x%5E3%20%2B%20x%5E2-6x)
1.112 for 10 inch and 1.2 for 6 inch so you get better price for buying 10 the inch pizza
Answer:
graph A
Step-by-step explanation: