Question

consider the graph of the polynomial function. which of the following shows three binomial factors of the function?

a) \\((x + 2)(x - 1)(x - 3)\\)

b) \\((x + 1)(x + 3)(x - 2)\\)

c) \\((x - 1)(x - 2)(x - 3)\\)

d) \\((x + 1)(x + 2)(x + 3)\\)

Explanation:

Identify the x-intercepts of the polynomial

Using the Polynomial Factors from Graphs knowledge point

$$ \text{The graph crosses the } x\text{-axis at } x = -2, \quad x = 1, \quad \text{and} \quad x = 3. $$

Relate the zeros to binomial factors

Using the Polynomial Factors from Graphs knowledge point

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Match with the given options

Using the Polynomial Factors from Graphs knowledge point

$$ \text{The three binomial factors are } (x + 2)(x - 1)(x - 3), \text{ which matches option A.} $$

Answer:

• A) \((x + 2)(x - 1)(x - 3)\) (Correct answer)
• B) \((x + 1)(x + 3)(x - 2)\)
• C) \((x - 1)(x - 2)(x - 3)\)
• D) \((x + 1)(x + 2)(x + 3)\)