Question

step 4 the first degree quotient is the third linear factor which will yield the third zero of the polynomial function. what is the linear factor? the factor is (x + 1 ). the zero of this factor is x = -1. step 5 finally, list all 3 zeros of the function. (enter your answers as a comma - separated list. include the given zero, 7i, in your answer.) x = submit skip (you cannot come back) resources read it

Explanation:

Step1: Recall complex conjugate root theorem

For polynomials with real coefficients, if \(a+bi\) is a zero, then \(a-bi\) is also a zero. Given \(7i\) (which is \(0+7i\)), its conjugate is \(-7i\).

Step2: Identify known zero

From Step 4, the third zero is \(x=-1\).

Step3: Compile all zeros

Combine the given zero, its conjugate, and the found real zero.

Answer:

\(x = -1, 7i, -7i\)