Polynomials: Factoring - XYZ Custom Plus

780Chapter 12 Polynomials: FactoringNote, in the second to last line, that we do not set 2 equal to 0. That is because 2can never be 0. It is always 2. We only use the zero-factor property to set variablefactors to 0 because they are the only factors that can possibly be 0.Also notice that it makes no difference which side of the equation is 0 when wewrite the equation in standard form.Although the equation in the next example is not a quadratic equation, it canbe solved by the method shown in the first five examples.6. Solve 8x 3 = 2x 2 + 10x.Example 6Solve 24x 3 = −10x 2 + 6x for x.SolutionFirst, we write the equation in standard form:24x 3 + 10x 2 − 6x = 02x (12x 2 + 5x − 3) = 02x (3x − 1)(4x + 3) = 0Standard formFactor out 2xFactor remaining trinomial2x = 0 or 3x − 1 = 0 or 4x + 3 = 0 Set factors to 0x = 0 or x = ​ 1 _3 ​ or x = − ​3 _4 ​ SolutionsAnswers5. −1, 3 6. 0, ​ 5 _After reading through the preceding section, respond in your ownwords and in complete sentences.1. When is an equation in standard form?2. What is the first step in solving an equation by factoring?3. Describe the zero-factor property in your own words.4. Describe how you would solve the equation 2x 2 − 5x = 12.4 ​, −1 Getting Ready for Class