Factor completely: 5c^(12)+4c^(6)s^(4)-9s^(8) Answer:

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Factor completely:  5c^(12)+4c^(6)s^(4)-9s^(8) Answer:

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Identify GCF: Look for a greatest common factor (GCF) in all three terms. The terms 5c^(12), 4c^(6)s^(4), and -9s^(8) do not have a common factor other than 1.Pattern Recognition: Since there is no GCF, we look for patterns or factor by grouping. The polynomial does not have a common number of terms to easily apply factor by grouping, but we can look for a pattern that resembles a difference of squares or a perfect square trinomial.Perfect Square Trinomial: Recognize that the polynomial is a trinomial and check if it is a perfect square trinomial. A perfect square trinomial takes the form (a^2 + 2ab + b^2) = (a + b)^2 or (a^2 - 2ab + b^2) = (a - b)^2. Our polynomial does not fit this pattern.Difference of Squares: Check if the polynomial can be factored as a difference of squares. A difference of squares takes the form a^2 - b^2 = (a + b)(a - b). The first term, 5c^(12), and the last term, -9s^(8), are both perfect squares, but the middle term, 4c^(6)s^(4), prevents us from using the difference of squares directly.Alternative Factoring Techniques: Look for a pattern that resembles a sum and difference of cubes or other factoring techniques. The polynomial does not fit the sum or difference of cubes pattern, and other common factoring techniques do not seem to apply.Substitution Method: Consider factoring by substitution if applicable. If we let u = c^(6) and v = s^(4), the polynomial becomes 5u^2 + 4uv - 9v^2. This looks like a quadratic in terms of u and v, which we can try to factor.Factor Quadratic: Factor the quadratic 5u^2 + 4uv - 9v^2. We look for two numbers that multiply to (5)(-9)v^2 = -45v^2 and add to 4v. These numbers are 9v and -5v.Write Binomials: Write the polynomial as two binomials using the numbers found in Step 7. (5u^2 + 9uv) + (-5uv - 9v^2) = 5u(u + 9v) - 5v(u + 9v)Factor Common Binomial: Factor out the common binomial factor (u + 9v). 5u(u + 9v) - 5v(u + 9v) = (5u - 5v)(u + 9v)Substitute Back Variables: Substitute back c^(6) for u and s^(4) for v. (5c^(6) - 5s^(4))(c^(6) + 9s^(4))Factor Out Common Factor: Factor out the common factor of 5 from the first binomial. 5(c^(6) - s^(4))(c^(6) + 9s^(4))Further Factorization: Recognize that c^(6) - s^(4) is a difference of squares and can be factored further. (c^(6) - s^(4)) = (c^(3) + s^(2))(c^(3) - s^(2))Final Factored Form: Write the final factored form of the polynomial. 5(c^(3) + s^(2))(c^(3) - s^(2))(c^(6) + 9s^(4))

Factor completely: $\newline$ $5 c^{12}+4 c^{6} s^{4}-9 s^{8}$ $\newline$ Answer:

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Factor completely:\newline5c12+4c6s4−9s8 5 c^{12}+4 c^{6} s^{4}-9 s^{8} 5c12+4c6s4−9s8\newlineAnswer:

Factor completely: $\newline$ $5 c^{12}+4 c^{6} s^{4}-9 s^{8}$ $\newline$ Answer: