Find an equation of a degree 3 polynomial (in factored form) with the given zeros of . Assume
the leading coefficient is 1 .

Ask by French Owen. in the United States

Mar 29,2025

Question

Find an equation of a degree 3 polynomial (in factored form) with the given zeros of $$ f(x):-3,3,4 $$. Assume the leading coefficient is 1 . $$ f(x)=\square $$

UpStudy AI · Accepted Answer

1. The zeros of the polynomial are given as $$-3$$, $$3$$, and $$4$$.

2. By the Factor Theorem, the corresponding factors of the polynomial are:
   - For the zero $$-3$$: $$x - (-3) = x + 3$$
   - For the zero $$3$$: $$x - 3$$
   - For the zero $$4$$: $$x - 4$$

3. Since the leading coefficient is $$1$$, the polynomial in factored form is:
   $$
   f(x) = (x + 3)(x - 3)(x - 4)
   $$

4. Thus, the equation of the degree 3 polynomial is:
   $$
   \boxed{f(x) = (x + 3)(x - 3)(x - 4)}
   $$
$$ f(x) = (x + 3)(x - 3)(x - 4) $$

Find an equation of a degree 3 polynomial (in factored form) with the given zeros of . Assume
the leading coefficient is 1 .

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Find an equation of a degree 3 polynomial (in factored form) with the given zeros of . Assume the leading coefficient is 1 .