4. Find a polynomial \( f(x) \) with a leading coefficient of -3 and \( f(-4)=0, f(2)=0 \) and \( f(1)=0 \). Write your answer in complete factored form.

To construct a polynomial \( f(x) \) with the required roots and leading coefficient, we start by utilizing the information given: 1. The roots of the polynomial are \( -4 \), \( 2 \), and \( 1 \). Hence, we can express the polynomial as: \[ f(x) = k(x + 4)(x - 2)(x - 1) \] where \( k \) is the leading coefficient. 2. We know that the leading coefficient should be \( -3 \). Thus, we set \( k = -3 \): \[ f(x) = -3(x + 4)(x - 2)(x - 1) \] 3. Now, we keep it in the complete factored form: \[ f(x) = -3(x + 4)(x - 2)(x - 1) \] So the polynomial \( f(x) \) in complete factored form is: \[ f(x) = -3(x + 4)(x - 2)(x - 1) \]