Answer:
2 square units
Step-by-step explanation:
We know that the area of a rectangle is:
[tex]A=(length)(width)[/tex]
And, givens are:
[tex]length=2x^{3} -5x^{2}+8\\width=x+3[/tex]
Replacing given expression:
[tex]A=(2x^{3} -5x^{2}+ 8)(x+3)[/tex]
So, to find the area, we need to solve that expression. The faster and easier way to do it is by graphing, given values to x-variable, and finding values for y-variable in return. Each pair represents a point. The graph is like the image attached.
In the graph, we observe that only has two solutions:
[tex](-3,0) (-1.06;0)[/tex]
Now, we test each one to find an area that make sense, that is, a positive area:
[tex]length=2(-3)^{3} -5(-3)^{2}+ 8\\width=-3+3=0[/tex]
We see that -3 makes the width zero, which don't make sense. So, we use -1.06, or just -1.
[tex]length=2(-1)^{3} -5(-1)^{2}+ 8=-2-5+8=1\\width=-1+3=2[/tex]
Therefore, the area is A=(2)(1)=2 square units
