Answer:
Please check the explanation.
Step-by-step explanation:
Given the equation
[tex]x^3-6x^2+3x+10=0[/tex]
Step 1:
Writing the equation
[tex]x^3-6x^2+3x+10=0[/tex]
Step 2:
In order to determine the x-intercept, we need to plot the graph.
All the values at y = 0 would be x-intercepts of the equation.
Please check the attached graph below.
Step 3:
It is clear from the graph, the points where y = 0, the x-values are: -1, 2 and 5.
Hence, (-1, 0) (2, 0) and (5, 0) are the x-intercepts of the equation.
Thus, x = -1, x = 2, and x = 5 are the solution of the equation.
Hence,
[tex]x^3-6x^2+3x+10=\left(x-2\right)\left(x+1\right)\left(x-5\right)[/tex]
