Factor completely: 6x^(4)-17x^(2)t^(2)+10t^(4) Answer:

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Factor completely:  6x^(4)-17x^(2)t^(2)+10t^(4) Answer:

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Recognize as quadratic form: Recognize the polynomial as a quadratic in form. The given polynomial 6x^(4)-17x^(2)t^(2)+10t^(4) can be seen as a quadratic in terms of x^2, where x^2 is the variable and t^2 is a constant.Factor using middle term: Factor the quadratic polynomial using the middle term factor method. We need to find two numbers that multiply to (6x^2)(10t^2) = 60x^2t^2 and add up to -17x^2t^2. The numbers that satisfy these conditions are -12x^2t^2 and -5x^2t^2.Rewrite by splitting: Rewrite the polynomial by splitting the middle term. 6x^(4)-17x^(2)t^(2)+10t^(4) = 6x^(4) - 12x^(2)t^(2) - 5x^(2)t^(2) + 10t^(4)Factor by grouping: Factor by grouping. Group the terms to factor by grouping: (6x^(4) - 12x^(2)t^(2)) - (5x^(2)t^(2) - 10t^(4)) Now factor out the common factors from each group: 6x^2(x^2 - 2t^2) - 5t^2(x^2 - 2t^2)Factor out common factor: Factor out the common binomial factor. The common binomial factor is (x^2 - 2t^2), so we factor it out: (6x^2 - 5t^2)(x^2 - 2t^2)Recognize difference of squares: Recognize that (x^2 - 2t^2) is a difference of squares and can be further factored. (x^2 - 2t^2) can be written as (x^2 - (sqrt(2)t)^2), which is a difference of squares and can be factored as: (x - sqrt(2)t)(x + sqrt(2)t)Write final factorization: Write the final factorization. The complete factorization of the polynomial is: (6x^2 - 5t^2)(x - sqrt(2)t)(x + sqrt(2)t)

Factor completely: $\newline$ $6 x^{4}-17 x^{2} t^{2}+10 t^{4}$ $\newline$ Answer:

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Factor completely:\newline6x4−17x2t2+10t4 6 x^{4}-17 x^{2} t^{2}+10 t^{4} 6x4−17x2t2+10t4\newlineAnswer:

Factor completely: $\newline$ $6 x^{4}-17 x^{2} t^{2}+10 t^{4}$ $\newline$ Answer: