Answer :
Final answer:
To solve the polynomial inequality without factoring, you can use a graphical method. By plotting the polynomial function and identifying where the graph is less than zero (beneath the x-axis), one can find the solution to the inequality. An understanding of parabolas and functions is key to this solution method.
Explanation:
The subject at hand is a form of mathematics known as quadratic functions, or second-order polynomials, expressed in the given equation y=x^2+4x^2-20x-48. To solve the polynomial inequality x^3+4x^2-20x-48 < 0 without factoring, you can utilize a graph. The graphical method allows us to visualize the behavior of the polynomial function and to identify ranges for which the function is negative.
When graphing, you are essentially plotting data pairs (x, y) where each y value is a result of the function's calculation with a specific x value. In the context of this question, look at the graphed function and find the areas on the x-axis for which the graph dips below the x-axis (y = 0). These will be the solutions to the inequality as those are the x values for which the function is less than zero.
To utilize the graph in this context, it requires a deeper understanding of how quadratic functions behave graphically. A core tenet of quadratic functions is that they form a 'U' shaped curve known as a parabola, which can help in identifying areas where the function dips beneath the x-axis.
Learn more about Solving Polynomial Inequality Graphically here:
https://brainly.com/question/29068785
#SPJ1
