Question

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)=

Answer 1

Answer:

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)