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yarga [219]
3 years ago
11

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

Mathematics
2 answers:
Rom4ik [11]3 years ago
8 0

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

juin [17]3 years ago
3 0

Answer:

<h2>2 square units </h2>

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

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