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embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

Factor `x^3+3x^2+5x+15` :

Factor two terms at a time:


Now (x+3) is a common factor of both remaining terms and can be factored out:


`x^2+5` does not factor in the reals -- it can be fully factored in the complex numbers:


crmhaske's profile pic

crmhaske | College Teacher | (Level 3) Associate Educator

Posted on

The equation can be factored as follows:      

               0x^2+5x + 15
                         5x + 15



There exists one real root at x=-3


a=3; b=6; c=5

b^2-4ac = 36-4(3)(5)=-24<0

Therefore there are no maximum or minimum points.

f''(x)=6x+6=0 -> x=-1

f''(0)=6>0 -> concave up for x>-1

f''(-2)=-6<0 -> concave down for x<-1

Therefore there is an inflection point at x=-1 where the graph changes from concave downwards to concave upwards


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