Expert: Sherman D. - 5/8/2007

Question
hiya thius question was answered for me but i dont understand how he
arrived at.. 2x^2-5x-3=0
...and then i was told he divided both side by 6...i dont understand why.

please advice, question and answer follows:


(i)  y=4x^3 - 15x^2 - 18x + 12

dy/dx = 12x^2 - 30x - 18

12x^2 - 30x - 18 = 0
2x^2 - 5x - 3 = 0

(2x + 1)(x - 3) = 0
x = -1/2,  x = 3

Answer
all he did was factored it to find the x-intercepts of the derivative

y = 4x^3 - 15x^2 - 18x + 12

y' = 12x^2 - 30x - 18

y' = 6(2x^2 - 5x - 3)

so yeah what you have done is correct.

basically its because if they are divisible by a common number, then divide them by it.

just like if you had -x^2 + 5x + 4 = 0, you would divide everything by -1 first before you try to factor it.