The final factorization is thus;
[tex]f(x)\text{ = (x-3)(4x-1)(x+4)}[/tex]Here, we want to factor the polynomial
From the question, we are told that k is a factor;
[tex]\begin{gathered} \text{if k = 3} \\ \text{that means x = 3 is a factor and that x-3 is the linear form} \end{gathered}[/tex]The given polynomial is a polynomial of degree 3; that means there are 3 linear factors
We already have the first factor and we are left with two others to determine
To determine these, we have to divide the given polynomial by the first linear factor
We can do this by the use of the long division method
We have the result of the long divison as follows;
Now, what we have left to factorize is the quadratic trinomial
We have this as;
[tex]4x^2+15x-4=4x^2+16x-x-4\text{ = 4x(x+4)-1(x+4) = (4x-1)(x+4)}[/tex]