Given that (x + 5) is a factor of the function f (x) = x^3 + x^2 - 17x + 15, find the zeros, and write f (x) in factored form.

The zeros are:

The fully factored form is f (x) =

The fully factored form of the function f (x) is : (x+5) (x-1) (x-3)

Step-by-step explanation:

Given function f (x) = x³+x²-17 x+15 is a third degree polynomial. Hence, it will have 3 zeros.

Also, (x+5) is the factor of given function.

⇒ (x+5) divides the function f (x).

∴ (x³+x²-17 x+15) : (x+5) = (x²-4 x+3) ... (1)

Now, we will factorize x²-4 x+3 to get other zeros of the function f (X).

x²-4 x+3 ⇔ x²-3 x-x+3

⇔ x (x-3) - 1 (x-3) ⇔ (x-1) (x-3) ... (2)

hence, x²-4 x+3 ⇔ (x - 1) (x-3)

From, equation (1), (2) the factors of f (x) = x³+x²-17 x+15 are (x - 1) (x-3) (x-5)