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11315 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015 Date: Lesson 17: Equations Involving Factored Expressions Nov 149:09 AM Do Now: Factor using the Greatest Common Factor method: 3y2 + 12y 3x(x – 4) + 6(x – 4) Factor using the Difference of Perfect Squares method: m2 – 9 x4 16 Oct 166:32 PM 1 11315 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015 Discuss... If I told you that the product of two numbers is 20, could you tell me anything about the two numbers? Would the numbers have to be 4 and 5? Would both numbers have to be smaller than 20? Would they both have to be positive? Nov 149:11 AM If I told you that the product of two numbers is zero, could you tell me anything about the two numbers? How could we phrase this mathematically? This is known as the zero-product property. Nov 149:14 AM 2 11315 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015 Example 1 Consider the equation (x−4)(x+3) = 0. Rewrite the equation as a compound statement. Find the two solutions to the equation. Nov 149:16 AM Example 2 Remember to factor prior to solving! Rewrite the equation as a compound statement. Solve for x. 2x2 − 10x = 0, Nov 149:18 AM 3 11315 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015 Example 3 Remember to factor prior to solving! Rewrite the equation as a compound statement. Solve for x. x(x−3) + 5(x−3) = 0 Nov 149:21 AM Example 4 Verify: (a − 5)(a + 5) = a2 - 25 Nov 149:21 AM 4 11315 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015 Example 5 Solve for x. x2 - 9 = 5(x - 3) Nov 149:21 AM Example 6 Notice how these 3 equations are related! Everyone Solve for x. x + 2 = 5 Team 1 Solve for x. x2 + 2x = 5x Team 2 Solve for x. x(5x - 20) + 2(5x - 20) = 5(5x - 20) Nov 149:21 AM 5 11315 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015 Example 7 Consider the equation (x−2)(2x−3)=(x−2)(x+5). Lulu chooses to multiply through by 1 and gets the answer x−2 x = 8. But Poindexter points out that x=2 is also an answer, which Lulu missed. What‛s the problem with Lulu‛s approach? (x−2)(2x−3)=(x−2)(x+5) Nov 149:29 AM Use factoring to solve the original equation for x. (x−2)(2x−3)=(x−2)(x+5) Nov 149:31 AM 6 11315 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015 Homework: Exercises 1–6 1) (x+1)(x+2) = 0 3) 2) (3x−2)(x+12) = 0 (x−3)(x−3) = 0 Nov 149:22 AM Homework continued: 4) (x+4)(x-6)(x-10) = 0 6) x(x−5) + 4(x−5) = 0 5) x2 − 6x = 0 Nov 149:27 AM 7 11315 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015 Exercises 7–9 Use factoring to solve the equation for x: 7) (x – 2)(2x – 3) = (x – 2)(x + 1). Nov 149:32 AM 8) Solve for w: (w+2)(w−5) = w2 − 4. Oct 268:41 PM 8 11315 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015 9) Solve for x: x2 + 2x = 5x Nov 149:35 AM 10) The square of a number plus 3 times the number is equal to 4. What is the number? Oct 268:43 PM 9 11315 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015 Nov 141:00 PM Oct 268:43 PM 10