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