Finding all values that equal 0

Question

Let q(x)=x^3+3x^2-144x+18

Find all values of x at which q'(x)=0

Answer 1

take the derivative and set equal to zero:

3x^2 + 6x -144 = 0

divide by 3

x^2 +2x- 48 = 0

factor

(x-6)(x+8) = 0

set each factor = 0, solve for x

x = 6 or -8

Answer 2

0 = 3x² + 6x - 144

A calculus student could solve this using Algebra 1 techniques.