Question

write a polynomial function of least degree with i\

1. 3, 2, -2

Explanation:

Step1: Recall the Factor Theorem

If \( r \) is a root of a polynomial, then \( (x - r) \) is a factor of the polynomial. Given the roots \( 3 \), \( 2 \), and \( -2 \), the corresponding factors are \( (x - 3) \), \( (x - 2) \), and \( (x + 2) \) (since \( x - (-2)=x + 2 \)).

Step2: Multiply the Factors

First, multiply \( (x - 2) \) and \( (x + 2) \) using the difference of squares formula \( (a - b)(a + b)=a^{2}-b^{2} \). Here, \( a = x \) and \( b = 2 \), so \( (x - 2)(x + 2)=x^{2}-4 \).

Then, multiply the result by \( (x - 3) \):

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Answer:

The polynomial function of least degree with roots \( 3 \), \( 2 \), and \( -2 \) is \( f(x)=x^{3}-3x^{2}-4x + 12 \)