Question

Find a polynomial function of degree 3 with -1, 3, 5 as zeros.
A) f(x) = x^3 - 7x^2 + 7x + 15
B) f(x) = 3x^3 + 7x^2 + 7x - 15
C) f(x) = x^3 + 9x^2 + 7x - 3
D) f(x) = x^3 + 7x^2 + 7x - 15

Answer 1

Ok if it has the zeros, -1, 3 and 5, that means it will be
(x+1)(x-3)(x-5)

Answer 2

\(\large {
x=\{ -1, 3, 5\}\to
\begin{cases}
x=-1\to {\color{brown}{ x+1}}=0\\
x=3\to {\color{brown}{ x-3}}=0\\
x=5\to {\color{brown}{ x-5}}=0
\end{cases}
\\ \quad \\
({\color{brown}{ x+1}})({\color{brown}{ x-3}})({\color{brown}{ x-5}})=0\\ \quad \\\implies ({\color{brown}{ x+1}})({\color{brown}{ x-3}})({\color{brown}{ x-5}})=\textit{original polynomial}
}\)

Answer 3

Now you multiply them and you have the function