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Suppose that $f(x)=x^{2}+4 x-21$
a. Write $f(x)=x^{2}+4 x-21$ in factored form.
\[
f(x)=
\]
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b. Determine the function's horizontal intercepts. Use a comma to separate your answers.
\[
x=
\]
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Step 1 ：Suppose that the function is given by \(f(x)=x^{2}+4 x-21\).

Step 2 ：To write the function in factored form, we need to factorize the quadratic equation \(x^{2}+4 x-21\). This can be done by finding two numbers that multiply to -21 (the constant term) and add to 4 (the coefficient of the x term).

Step 3 ：The factored form of the function \(f(x)=x^{2}+4 x-21\) is \(f(x) = (x - 3)(x + 7)\).

Step 4 ：The horizontal intercepts of a function are the x-values where the function equals zero. This can be found by setting the factored form of the function equal to zero and solving for x.

Step 5 ：The function's horizontal intercepts are \(x = -7, 3\).

Step 6 ：\(\boxed{f(x) = (x - 3)(x + 7)}\)

Step 7 ：\(\boxed{x = -7, 3}\)