Solve: 6x3 + 12x17x2This equation is not quadratic, because it contains a term involving x. However, we can solve it by using factoring. First we get 0 on the right side by subtracting17x2 from both sides. Then we factor the polynomial on the left side and use an extension of the zero-factor property.To use the zero-factor property, we need one side of the equation to be factored completely and the other side to be 0.6x3 + 12x = 17x?This is the equation to solve.6x3|x2 + 12x = 17x² – 17x2To get 0 on the right side, subtract 17x² from both sides.6x3 – 17x2 + 12x = 0Combine like terms: 17x2 – 17x2 = 0.-x(6x2 – 17x + ) = 0x(2x –)(3x – 4) = 0Factor out the GCF, x.Factor the trinomial, 6x217x + 12.If x(2x – 3)(3x – 4) = 0, then at least one of the factors is equal to 0.х%3D 0 or 2х — 3 %3D 0or 3xSet each factor equal to 0.= 02x =X = 4Solve each equation.X =X =The solutions are 0, 3/2, and 4/3 and the solution set is {0, 4/3, 3/2}. Check each solution in the original equation, 6x3 + 12x =17x2.Solve: 10x3 –x²= 2xX =(smallest value)X =X =(largest value)

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Solve: 6x3 + 12x = 17x2 This equation is not quadratic, because it contains a term involving x. However, we can solve it by using factoring. First we get 0 on the right side by subtracting 17x2 from both sides. Then we factor the polynomial on the left side and use an extension of the zero-factor property. To use the zero-factor property, we need one side of the equation to be factored completely and the other side to be 0. 6x3 + 12x = 17x² 6x3 -Ox2 + 12x = 17x² – 17x² This is the equation to solve. To get 0 on the right side, subtract 17x2 from both sides. 6x3 – 17x2 + 12x = 0 Combine like terms: 17x2 – 17x² = 0. x(6x2 – 17x + ) = 0 Factor out the GCF, x. x(2x – -| )(3x – 4) = 0 Factor the trinomial, 6x² – 17x + 12. If x(2x – 3)(3x – 4) = 0, then at least one of the factors is equal to 0. x = 0 or 2x - 3 = 0 or 3x -O= 0 Set each factor equal to 0. 2x = X= 4 Solve each equation. X = The solutions are 0, 3/2, and 4/3 and the solution set is {0, 4/3, 3/2}. Check each solution in the original equation, 6x3 + 12x = 17x2. Solve: 10x3 – x² = 2x X = (smallest value) X = | (largest value) %3D