Algebra-2

To determine the correct factored form of a polynomial with the given roots -5, -6i, and 10, we need to consider that:

The root -5 corresponds to the factor x + 5.

The root 10 corresponds to the factor x - 10.

The root -6i must also have its conjugate 6i as a root, resulting in the factors x + 6i and x - 6i.

Thus, the correct factored form for the polynomial with these roots will include both the conjugate complex roots.

Step 1: Write the Factored Form

The correct factors corresponding to the roots are:

For the root -5: x + 5.

For the root 10: x - 10.

For the roots -6i and 6i: (x + 6i)(x - 6i).

So the overall factored form will be:

P(x) = (x + 5)(x - 10)(x + 6i)(x - 6i)

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