Question 955134
The roots are 5, 8, and -3


So the factors are (x-5), (x-8), (x+3)


Multiply everything out


(x-5)(x-8)(x+3)
(x-5)(x^2-5x-24)
x(x^2-5x-24)-5(x^2-5x-24)
x^3-5x^2-24x-5x^2+25x+120
x^3-10x^2+x+120


Let's see what the graph looks like


{{{ drawing(500, 500, -10, 10, -200, 200,graph( 500, 500, -10, 10, -200, 200,0,x^3-10x^2+x+120))}}}


that's the opposite of what we want, so simply flip it over the x axis to get


{{{ drawing(500, 500, -10, 10, -200, 200,graph( 500, 500, -10, 10, -200, 200,0,-x^3+10x^2-x-120))}}}


Algebraically, you are multiplying EVERY term by -1 so


x^3-10x^2+x+120 turns into -x^3+10x^2-x-120


The final answer is y = -x^3+10x^2-x-120

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