For the polynomial below, -2 is a zero.

f(x) = x^3 - 2x^2 - 6x + 4

Express f(x) as a product of linear factors.

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f(x) = x^{3} + (2x^{2} – 4x^{2} ) - (8x + 2x) + 4

= x^{3} + 2x^{2} – 4x^{2} - 8x + 2x + 4

= (x^{3} + 2x^{2} ) – (4x^{2} - 8x) + (2x + 4)

= x^{2}(x + 2) – 4x( x + 2) + 2 (x + 2)

= (x + 2)(x^{2 }– 4x + 2)

The answer for this question usually involves radicals if that helps any. That answer isn't correct on mine

factor x^{2 }– 4x + 2 = -(-x + sqrt(2) + 2)(x + sqrt(2) - 2)

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