Given that f(x) = 5x2 − 100, find x.

Here we have that f(x) = 5x^2 - 100 and we want to find x, this would mean, isolate the value of x.

First, we add 100 in both sides of the equation to remove the leftmost therm:

f(x) + 100 = 5x^2 - 100 + 100 = 5x^2

Now, we divide by 5 in both sides.

(f(x) + 100)/5 = (5x^2)/5 = x^2

Now, we apply the square root in both sides:

(+/-)√((f(x) + 100)/5) = √x^2 = x

Now you have the value of x, when someone gives you the value of f(x), you can find the two values of x asociated with it (there are two values of x asociated because f(x) is a quadratic function

(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