The area of a triangle is calculated by taking half the product of the base b and the height h.
A= 12 b hIn our case, the area of a triangular sail is 16x^4-60x^3-28x^2+56x-32 square meters, and its base is x-4 meters. We are asked to find the height of the sail. Let's substitute the expressions into the formula for the area and solve it for h.
Now, we want to divide two polynomials. You can use polynomial long division or a synthetic division. After the division, we get the following.
h=32x^4-120x^3-56x^2+112x-64/x-4
⇓
h= 32x^3+8x^2-24x+16
Therefore, the height of the sail is 32x^3+8x^2-24x+16 meters.
Extra
Synthetic Division
We will show how to divide 16x^4-60x^3-28x^2+56x-32 by x-4 using polynomial synthetic division. Remember that the general form of the synthetic division divisor must be x-a. Since the given divisor is already written in this form, we are ready to go.
rl IR-0.15cm r 4 & |rr 32 &- 120 &- 56& 112 &- 64 & & & & & c
The quotient is a polynomial of degree 3, with the above coefficients. The remainder is 0.
Quotient & Remainder
32x^3+8x^2-24x+16 & 0
Therefore, our expression can be written in the following form.
32x^4-120x^3-56x^2+112x-64/x-4
⇕
32x^3+8x^2-24x+16
