I need to factorise this completely, f(x)= x^3+x^2-4x-4 hence I need to solve this equation x^3+x^2-4x-4, can anybody help me factise this please, its just a short question on an engineering course I don't know where to start.
Put simple, the factor theorem states that for a polynomial of degree n
$\displaystyle x^n+c_{n-1}x^{n-1}+...+c_{2}x^2+c_{1}x+c_{0}$
(note, the leading coefficient is 1)
The roots of the polynomial are factors of c_{0}
I'll demonstrate this for n=3 like your question. With roots a, b and c you should be able to factorise the equation into
$\displaystyle (x-a)(x-b)(x-c)$
This expands to
$\displaystyle x^3+(-a-b-c)x^2+(ab+bc+ac)x-abc$
You can see that the three roots multiply to give the constant term in the polynomial. So they must be factors of the constant term.
In your equation -4 is the constant term. The factors are 1,-1,2,-2,4,-4. Try putting each of these factors into the equation and if the result is zero you know its a root. If only one of these is a root you will have to do long division in algebra to get a quadratic which has the other two roots.
Spoiler:
Andrew
get the free term of the equation -4 and find which numbers divide it . you will find +1,-1,+2,-2,+4,-4 .
then get each number and substitute in the given polynomial to see which one gives zero .
if p(x) = x^3+x^2-4x-4 then you will find p(-2)=0 ,p(+2)=0 and p(-1) =0 .
consequently this polynomial can be factorized : p(x) =(x-2)(x+2)(x+1)
as simple as such.
READ CAREFULLY THE INSTRUCTIONS THAT SHAKARRI POSTED BEFORE ME TO HAVE A GENERAL IDEA HOW A POLYNOMIAL OF N DEGREE CAN BE FACTORIZED.
MINOAS