Answer:
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Step-by-step explanation:
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The factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)
<h3>How to determine the factors?</h3>
The expression is given as:
x^3 + 4x^2 +5x + 20
Group the expression into two
(x^3 + 4x^2) + (5x + 20)
Factorize each group
x^2(x + 4) + 5(x + 4)
Factor out x + 4
(x^2 + 5)(x + 4)
Hence, the factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)
Read more about expressions at:
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Using translation concepts, it is found that the function g that reflects f across the x-axis is given by:
![g(x) = -x^3 - 9x^2 + 3x + 1](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-x%5E3%20-%209x%5E2%20%2B%203x%20%2B%201)
<h3>What is a translation?</h3>
- A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
- A reflection across the x-axis means that the function is <u>multiplied by -1</u>.
In this problem, the function is:
![f(x) = x^3 + 9x^2 - 3x - 1](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E3%20%2B%209x%5E2%20-%203x%20-%201)
With the reflection across the x-axis, it is multiplied by -1, and hence:
![g(x) = -x^3 - 9x^2 + 3x + 1](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-x%5E3%20-%209x%5E2%20%2B%203x%20%2B%201)
You can learn more about translation concepts at brainly.com/question/20720324
Answer:
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Step-by-step explanation:
The easiest way to graph this equation is using the x and y intercepts. Plug zero in for x to solve for y, then plug zero in got y to solve for x.