Find a polynomial function of degree 4 with the zeros -3 (multiplicity 2 ) and 3 (multiplicity 2), whose graph passes through the point $(- 4, 196)$ .
$f (x) =$
(Simplify your answer. Use integers or fractions for any numbers in the expression.)

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Answer

So, the polynomial function of degree 4 with the zeros -3 (multiplicity 2 ) and 3 (multiplicity 2), whose graph passes through the point $(- 4, 196)$ is $f (x) = 4 (x + 3)^{2} (x - 3)^{2}$ .

Steps

Step 1 ：The polynomial function of degree 4 with the given zeros can be written in the form of $f (x) = a (x + 3)^{2} (x - 3)^{2}$ .

Step 2 ：To find the value of $a$ , we can substitute the point $(- 4, 196)$ into the function and solve for $a$ .

Step 3 ：After solving, we find that $a = 4$ .

Step 4 ：So, the polynomial function of degree 4 with the zeros -3 (multiplicity 2 ) and 3 (multiplicity 2), whose graph passes through the point $(- 4, 196)$ is $f (x) = 4 (x + 3)^{2} (x - 3)^{2}$ .

Find a polynomial function of degree 4 with the zeros -3 (multiplicity 2 ) and 3 (multiplicity 2), whose graph passes through the point (−4,196).f(x)=(Simplify your answer. Use integers or fractions for any numbers in the expression.)

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Find a polynomial function of degree 4 with the zeros -3 (multiplicity 2 ) and 3 (multiplicity 2), whose graph passes through the point $(- 4, 196)$ .
$f (x) =$
(Simplify your answer. Use integers or fractions for any numbers in the expression.)