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Answer :
Final answer:
The equation 6x^(3)+48x^(2)+96x=0 can be factored to 6x(x² + 8x + 16) = 0. Setting each factor equal to zero, we get 6x = 0 and x = -4 as the solutions, by applying the quadratic formula.
Explanation:
To solve the given Solving polynomial equation , we can factor out the common factor of each term, which in this case is 6x. Factoring out gives us 6x(x² + 8x + 16) = 0.
Next, we use the zero-product property to equate each factor to zero: So, 6x = 0 and x² + 8x + 16 = 0. For the latter equation, we can apply the quadratic formula -b ± √b² - 4ac / 2a to find the roots, where a, b, c are coefficients of the quadratic terms, linear terms and constant terms respectively.
In our case, a = 1, b = 8, c = 16. Solving these gives us x = -4 and x = 0 as the solutions for the original equation.
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