Question

find the zeros of the polynomial below.
$(x - 2)(x + 3)(x + 5)$
\\(\\{ -2, 3, 5\\}\\)
\\(\\{ -5, -3, -2\\}\\)
\\(\\{ 2, 3, 5\\}\\)
\\(\\{ -5, -3, 2\\}\\)

Explanation:

Step1: Recall the zero - product property

The zero - product property states that if \(ab = 0\), then either \(a=0\) or \(b = 0\) (or both). For a polynomial in factored form \((x - a)(x - b)(x - c)\), the zeros of the polynomial are the values of \(x\) that make each factor equal to zero.

Step2: Find the zeros by setting each factor to zero

• For the factor \((x - 2)\):

Set \(x-2=0\). Solving for \(x\), we add 2 to both sides of the equation: \(x=2\).

• For the factor \((x + 3)\):

Set \(x + 3=0\). Solving for \(x\), we subtract 3 from both sides of the equation: \(x=-3\).

• For the factor \((x + 5)\):

Set \(x + 5=0\). Solving for \(x\), we subtract 5 from both sides of the equation: \(x=-5\).

So the zeros of the polynomial \((x - 2)(x + 3)(x + 5)\) are \(x = 2\), \(x=-3\) and \(x=-5\), which can be written as the set \(\{-5,-3,2\}\).

Answer:

\(\{-5,-3,2\}\) (the option corresponding to \(\{-5,-3,2\}\))