Given our function f(x) = x^3 + 2x^2 - 5x - 6 the shaded region required is the sum of two areas which we will call A (shaded region above the x axis) and B (shaded region below the x axis).

To find A we need to integrate f(x) with respect to x between two limits i.e. from the lowest value of x for region A, to the greatest value of x for region A.

To find these limits we must calculate the values of x at which f(x) cuts across the x axis, and as you know, these are the roots of our cubic equation.

There are a number of ways to find the roots of our equation - the easiest approach in this case seems to be by factorising the cubic.

To factorise f(x) we can use the polynomial factor theorem which tells us that:

if f(a) = 0 then (x-a) is a factor of f(x).

From your graph you might consider the value: a = -1

f(-1) = (-1)^3 + 2(-1)^2 -5(-1) - 6
= 0

This satisfies the condition of the factor theorem so:
=> (x - (-1)) is a factor of f(x).

We can use this to factorise f(x) completely and so find all the roots:

1. Find thearea of theshadedregion on the following geoboard if the unit of measurement is 1 cm2.
2. For each of the following, can the measures represent sides of a right triangle? Explain your answers.

What is thearea of theshadedregion between the two squares
One smaller square is inside a larger square. The remaining open area is theshadedregion. What is thearea of this shadedregion?
smaller square: each side is 3.2cm
larger square: each side is 9.5cm

1. Find thearea of the triangle.
2. There is a shaded triangular prism 6in x 8in x 11in with a rectangle solid 3in x 4in x 11in not shaded. Find the volume of theshadedarea.
3. Given thegraph, name an edge that is a bridge, if any.
4. Find thearea in meters of a trapezoid with a height of 4 m and bases of 8 m and

Find thearea of theshadedregion. Answer to the nearest tenth.
Picture a square. The arcs have their centers at opposite vertices of the square and that is theregion that is shaded . The base says 4 yds.

The picture is just of a square 3/4 of the square is shaded if I can get help with that information thank you you will not be able to see the picture of the square.
1. Area of a square. Find a polynomial A(x) that represents
thearea of theshadedregion in the accompanying figure.
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Please help with the following questions:
1. Use the limit process to find thearea of theregion between thegraph of the function and the axis over the given interval. Sketch theregion.
y = 4 - x^2, [-2,2]
2. Find thearea of theregion bounded by thegraphs of the equations.
y = x^3 + x, x = 2, y = 0

88. Area of a square. Find a polynomial A(x) that represents thearea of theshadedregion in the accompanying figure.
96. Compounded semiannually. P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial P(1 + r/2)^2 represents the value of the investment af

Question:
Graphthe following costraints (use graph for yourself)
1) 3x1 + 3x2 <= 300
2) 6x1 + 3x2 <= 480
3) 3x1 + 3x2 <= 480
x1 & x2 >= 0
a) Do we have Feasible Region?
b) Identify the value of each point of feasible area. Explain in detail.