For the following exercises, use the given information about the polynomial graph to write the equation. Degree 3. Zeros at x = −2, x = 1, and x = 3.

${\displaystyle f\left(x\right)=100{\left(1.25\right)}^x}$
Is it true or false, the growth factor is 25%? If not, what is and what is 25%?

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 5. Roots of multiplicity 2 at $x=minus;3$ and $x=2$ and a root of multiplicity 1 at $x=minus;2$. y-intercept at (0, 4).

Graph the polynomial by transforming an appropriate graph of the form ${\displaystyle y=x^n}$. Show clearly all x- and y-intercepts. ${\displaystyle P\left(x\right)=-3{(x+2)}^5+96}$

Find the cubic polynomial whose graph passes through the points ${\displaystyle (-1,-1),(0,1),(1,3),(4,-1).}$

Graph the polynomial by transforming an appropriate graph of the form ${\displaystyle y=x^n}$.
Show clearly all x- and y-intercepts. ${\displaystyle P\left(x\right)=81-{(x-3)}^4}$

Every cubic polynomial can be categorised into one of four types: Type 1: Three real, distinct zeros: ${\displaystyle P\left(x\right)=a(x-\alpha )(x-\beta )(x-\gamma ),a\ne 0}$
Type 2: Two real zeros, one repeated: ${\displaystyle P\left(x\right)=a(x-\alpha )2(x-\beta ),a\ne 0}$
Type 3: One real zero repeated three times: ${\displaystyle P\left(x\right)=a(x-\alpha )3,a\ne 0}$
Type 4: One real and two imaginary zeros: ${\displaystyle P\left(x\right)=(x-\alpha )(ax2+bx+c),\Delta =b2-4ac<0,a\ne 0}$
Experiment with the graphs of Type 1 cubics. Clearly state the effect of changing both the size and sign of a. What is the geometrical significance of $\alpha ,\beta ,and\gamma ?\alpha ,\beta ,and\gamma$?

Consider the following problem: A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens? Draw several diagrams illustrating the situation, some with shallow, wide pens and some with deep, n\Rightarrow pens. Find the total areas of these configurations. Does it appear that there is a maximum area? If so estimate it