Which of the following equations represents a graph that decreases most rapidly?

a. y=-5x^2-6x-1
b. y=(3/4)x^2-4x-3
c. y=-x^2+13x-36
d. y=3x^2-23x-14

A) y = -5*x^2 - 6*x - 1

Step-by-step explanation:

For this, we need to look at the coefficient that multiplicates the biggest degree in the polynomial (in this case is the coefficient that is in multiplicates the x^2)

If we want the graph that decreases most rapidly, we need to look to the biggest negative number.

The biggest negative coefficient is the -5 in the first option

Then the correct option is A) y = -5*x^2 - 6*x - 1

(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