Question

The length of a rectangle is represented by the polynomial 2x3 – 5x2 + 8 and the width is represented

Answer 1

1) the polynomial representing the area is

2x^4 + 6x^3 - 5x^2 -7x + 24

2) the constant term is

24

3) the polynomial is a 4th degree

4) if my guess is ryt... the LEADING coefficient is the coefficient of the highest degree of X ...i.e 2

Answer 2

Answer:

2 square units

Step-by-step explanation:

We know that the area of a rectangle is:

$A=(length)(width)$

And, givens are:

$length=2x^{3} -5x^{2}+8\\width=x+3$

Replacing given expression:

$A=(2x^{3} -5x^{2}+ 8)(x+3)$

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:

$(-3,0) (-1.06;0)$

Now, we test each one to find an area that make sense, that is, a positive area:

$length=2(-3)^{3} -5(-3)^{2}+ 8\\width=-3+3=0$

We see that -3 makes the width zero, which don't make sense. So, we use -1.06, or just -1.

$length=2(-1)^{3} -5(-1)^{2}+ 8=-2-5+8=1\\width=-1+3=2$

Therefore, the area is A=(2)(1)=2 square units