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, <u><em>(x+5) </em></u>is the factor of given function.
⇒(x+5) divides the function f(x).
∴ <em>(x³+x²-17 x+15) ÷ (x+5) = (x²-4 x+3) </em> ......(1)
Now, we will factorize x²-4 x+3 to get other zeros of the function f(X).
<em>x²-4 x+3 ⇔ x²-3 x-x+3</em>
⇔ <em>x(x-3)-1(x-3) ⇔ (x-1)(x-3)</em> ....(2)
hence, <em>x²-4 x+3 ⇔ (x -1)(x-3)</em>
From, equation (1),(2) the factors of<u><em> f(x) = x³+x²-17 x+15 are (x -1)(x-3)(x-5)</em></u>
