Question

Factor f(x) into linear factors given that k is a zero of f(x).f(x) = 4x3 + 3x2 - 49x + 12; k= 3f(x) =(Factor completely.)

Answer 1

The final factorization is thus;

`f(x)\text{ = (x-3)(4x-1)(x+4)}`

Here, we want to factor the polynomial

From the question, we are told that k is a factor;

`\begin{gathered} \text{if k = 3} \\ \text{that means x = 3 is a factor and that x-3 is the linear form} \end{gathered}`

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;

`4x^2+15x-4=4x^2+16x-x-4\text{ = 4x(x+4)-1(x+4) = (4x-1)(x+4)}`