Please Please Please help!
f(x) = x^3 + 4x^2 - x - 4
What are the factors of f(x)? Show your work.
What are the zeros of f(x)? Show your work.
What are the steps you would follow to graph f(x)?

Question

Please Please Please help!
f(x) = x^3 + 4x^2 - x - 4
What are the factors of f(x)? Show your work.
What are the zeros of f(x)? Show your work.
What are the steps you would follow to graph f(x)?

campbell_st · Answer

well it looks like if you group in pairs you get 

$$f(x) =( x^3 - x) + (4x^2 -4) $$

factor the binomials and you get

$$f(x) = x(x^2 -1) + 4(x^2 -1)$$

which can be written as 

$$f(x) = (x + 4)(x^2 - 1)$$

you just need to further factor the quadratic to get the solution.

campbell_st · Answer

so once you have the factors you need to set each binomial factor to zero and find the zero

 x + 4 = 0     so x = -4 is a factor. 

the to sketch the graph,    

find the 1st derivative and set it to zero and solve for x, these will be the stationary points. 

find the 2nd derivative set it to zero and solve for x. 

substitute the 1st derivative solutions into the 2nd derivative to find the types of stationary points, max or min. 

check either side of the 2nd derivative solution so make sure there is a change in concavity... if so you have a point of inflexion. 

lastly set x = 0 in the original equation to find the y-intercept. 

hope this helps

anonymous · Answer

Thank you SO MUCH! This helped more than anything!!!