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Jan. 31, 2023•0 likes•2 views

Jan. 31, 2023•0 likes•2 views

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Find all of the real zeros of the polynomial function, then use the real zeros to factor f over the real numbers. f(x) = 3x^4 - 6x^3 + 4x^2 - 2x + 1 Solution zero\'s =1,+ i/3,_i/3 OR x=1,1,-i/3,i/3 f \' (x) = 12x^2 + 6x - 6 Find Critical Values: 0 = 12x^2 + 6x - 6 0 = 6(2x^2 + x - 1) 0 = 6(2x - 1)(x + 1) x = 1/2, -1 Intervals: (-infinity, -1)----positive----increasing (-1, 1/2)----------negative--decreasing (1/2, infinity)----positive---increasing .

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- 1. Find all of the real zeros of the polynomial function, then use the real zeros to factor f over the real numbers. f(x) = 3x^4 - 6x^3 + 4x^2 - 2x + 1 Solution zero's =1,+ i/3,_i/3 OR x=1,1,-i/3,i/3 f ' (x) = 12x^2 + 6x - 6 Find Critical Values: 0 = 12x^2 + 6x - 6 0 = 6(2x^2 + x - 1) 0 = 6(2x - 1)(x + 1) x = 1/2, -1 Intervals: (-infinity, -1)----positive----increasing (-1, 1/2)----------negative--decreasing (1/2, infinity)----positive---increasing