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Write the polynomial as a product of linear factors (in completely factored form) given x + 2 is a factor.

p(x) = 3x^4 + 4x^3 - x^2 + 4x - 4

please help me =,(

1 answer

Use either long algebraic division or synthetic divsion by x+2 to show
3x^4 + 4x^3 - x^2 + 4x - 4
= (x+2)(3x^3 - 2x^2 + 3x - 2)
= (x+2)(x^2(3x - 2) + (3x-2)) , grouping
=(x+2)(3x-2)(x^2 + 1)
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