PLEASE ANSWER BUT TAKE YOUR TIME. Write an equation for a polynomial with all the following features:

a. The degree is 5.

b. The polynomial has 4 terms.

c. The graph of the polynomial crosses the vertical axis at Y = 12 .

Identify the approximate input values of any relative maximums and minimums of this 5th degree polynomial.

Step-by-step explanation:

(x-1)^5 = x^5 - 5x^4 + 15x^3 - 15x^2 + 5x - 1

That has 6 terms, so let's get rid of the two middle ones.

f(x) = (x-1)^5 - 15x^2(x-1)

Now, f(0) = 1, but we want f(0) = 12

So, let

f(x) = 12((x-1)^5 - 15x^2(x-1)) = 12x^5 - 60x^4 + 60x - 12

As for the graph, it looks like

y = (x+4)(x+2)(x-1)^2(x-6)

The extrema appear to be at about (-3,1), (-1,-1), (1,0), (4,-9)

ye

step-by-step explanation:

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0