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)

Answered: Image /qna-images/answer/7170c68d-ccd9-4ecb-981d-0e8c2a907062.jpg

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

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

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

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 = 17x?
This is the equation to solve.
6x3
|x2 + 12x = 17x² – 17x2
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
x(2x –)(3x – 4) = 0
Factor out the GCF, x.
Factor the trinomial, 6x2
17x + 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 0
or 3x
Set each factor equal to 0.
= 0
2x =
X = 4
Solve 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
= 2x
X =
(smallest value)
X =
X =
(largest value)

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