Is g(x) = x(x - 4)[x-i(square root of 7)][x+i(square root of 7)] the factored form of f(x) = x^4+4x^3+7x^2+28x

No.

It's  x^4 - 4x^3 + 7x^2 - 28x.

Step-by-step explanation:

(x - √7 i)(x +√7i)

= x^2 + √7x i - √7x i - 7 i^2

= x^2 - 7 * -1

= x^2 + 7

g(x) = x(x - 4)(x^2 + 7)

= x(x^3 + 7x - 4x^2 - 28)

= x^4 - 4x^3 + 7x^2 - 28x.

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i

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step-by-step explanation: