Question

Please leave a real answer it would be very helpful

Answer 1

The polynomial that represents the length is:

h(x) = 11x + 1.

How to find the length?

We know that the area of the top surface is given by:

f(x) = 66x^2 + 17x + 1

And the width of the top surface is:

g(x) = 6x + 1.

We can assume that the length, h(x), is another polynomial of degree 1, so we can write:

h(x) = a*x + b

Now, the area is the product of the width and the length, so we have:

f(x) = g(x)*h(x)

f(x) = (6x + 1)*(ax + b)

     =   6ax^2 + (6b)x + (a)x + b

     =   (6a)x^2 + (6b + a)x + b

Now let's compare this with f(x), correspondent coefficients must have the same value.

66x^2 + 17x + 1 = (6a)x^2 + (6b + a)x + b

Then we have:

66 = 6a

17 = 6b + a

1 = b

From the first equation we have:

66/6 = a = 11

And from the third:

b = 1

Then the length is:

h(x) = 11x + 1.

If you want to learn more about polynomials, you can read:

brainly.com/question/4142886