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

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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.

`y=x(x-6)(x+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:

first factor out x

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

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

x(x^2-6x+2x-24)

=x(x(x-6)+2(x-6))

=x(x+2)(x-6)

at x intercepts, y = 0

y=x(x+2)(x-6)

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

x intercepts are 0, -2 and 6