To find a polynomial \( f(x) \) of degree 4 that has the given zeros \( 5, -3, 7, \) and \( -4 \), you can express the polynomial in factored form using these zeros.
The general form of a polynomial based on its zeros \( r_1, r_2, r_3, r_4 \) is given by:
\[ f(x) = k(x - r_1)(x - r_2)(x - r_3)(x - r_4) \]
Here, \( k \) is a constant (which we typically set to 1 for a monic polynomial). The roots provided are:
- \( r_1 = 5 \)
- \( r_2 = -3 \)
- \( r_3 = 7 \)
- \( r_4 = -4 \)
Thus, the polynomial \( f(x) \) can be written as:
\[ f(x) = (x - 5)(x + 3)(x - 7)(x + 4) \]
This is the polynomial in factored form with the specified zeros.
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