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

Question

Catherine Strong

Mathematics

27 June, 18:22

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

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Answers (1)

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Tianna Larsen · Answer 1

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.