The polynomial 3x ^ 3 - 16x ^ 2 + 31x - 20 the area of a trapezoidal desktop. Of the bases of the x ^ 3 - 5x the height of the trapezoid? Hins: Use long division, what is trapezoid represented by the expressions trapezoid

Step-by-step explanation:

Given:

Area = 3x^3 - 16x^2 + 31x - 20

Base:

x^3 - 5x

Area of trapezoid, S = 1/2 * (A + B) * h

Using long division,

(2 * (3x^3 - 16x^2 + 31x - 20)) / x^3 - 5x

= (6x^3 - 32x^2 + 62x - 40)) / x^3 - 5x = 6 - (32x^2 - 92x + 40) / x^3 - 5x = 2S/Bh - Ah/Bh

= 2S/Bh - A/B

= (2S/B * 1/h) - A/B

Since, x^3 - 5x = B

Comparing the above,

A = 32x^2 - 92x + 40

2S/B = 6

Therefore, h = 1