Factor this polynomiala to determine the x intercepts and graph it.   y = x^3 - 2x^2 - 24x

Expert Answers
embizze eNotes educator| Certified Educator

Find the x-intercepts and graph `y=x^3-2x^2-24x` :

First factor out the largest common factor -- in this case it is x

`y=x(x^2-2x-24)` To factor the trinomial, we find two numbers whose product is -24 and whose sum is -2. The numbers are -6 and 4.


To find the x-intercepts let y=0 and use the zero product property:

x=0 or x-6=0 ==> x=6 or x+4=0 ==> x--4

Thus the three x-intercepts are -4,0,and 6. The y-intercept is 0.

Since this is a cubic with positive leading coefficient, the graph rises as x increases.

The graph:

mufarochamu | Student

first factor out x

polynomial becomes x(x^2-2x-24)

then factorise function in brackets using the factors of 24, 6 and 4




at x intercepts, y = 0


x=0 x+2=0 x-6=0

x intercepts are 0, -2 and 6