Developmental Mathematics Third Edition, Elayn Martin-Gay Sec. 13.1

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1 Developmental Mathematics Third Edition, Elayn Martin-Gay Sec Section 13.1 The Greatest Common Factor and Factoring by Grouping Complete the outline as you view Lecture Video Pause the video as needed as you fill in all blanks. Circle your answer to each numbered eercise. Then press Play to continue listening to Objective A Find the greatest common factor (GCF) of a list of numbers. Finding the GCF of a List of Integers Step 1: Step : Step 3: A number is a natural number other than 1 whose only factors are 1 and itself. 1. Find the GCF of 36 and 90. Objective B Find the GCF of a list of terms.. Find the GCF of 3,, and 5. The GCF of common variable factors is the variable raised to the eponent. Copyright 015 Pearson Education, Inc. 31

2 Developmental Mathematics Third Edition, Elayn Martin-Gay Sec Section 13.1 The Greatest Common Factor and Factoring by Grouping 3. Find the GCF of 4 1y and 3 0 y. Objective C Factor the GCF from the terms of a polynomial. Factor y+ y y means writing as a product. 6. y( + ) + 3( + ) 3 Copyright 015 Pearson Education, Inc.

3 Developmental Mathematics Third Edition, Elayn Martin-Gay Sec Section 13.1 The Greatest Common Factor and Factoring by Grouping Objective D Factor a polynomial by grouping. Factor by grouping. 7. 5y 15 6y + 18 To Factor by Grouping Step 1: Step : Step 3: Step 4: 8. 6a + 9ab + 6ab+ 9b 3 Copyright 015 Pearson Education, Inc. 33

4 Developmental Mathematics Third Edition, Elayn Martin-Gay Sec. 13. Section 13. Factoring Trinomials of the Form + b+ c Complete the outline as you view Lecture Video 13.. Pause the video as needed as you fill in all blanks. Circle your answer to each numbered eercise. Then press Play to continue listening to Objective A Factor trinomials of the form means writing as a product. + b + c. Factoring a Trinomial of the Form The product of + b+ c is: + b+ c= + + ( )( ) The product of the missing numbers is c. The sum of the missing numbers is b. + b + c Order of factors makes no difference. (Multiplication is.) Copyright 015 Pearson Education, Inc.

5 Developmental Mathematics Third Edition, Elayn Martin-Gay Sec. 13. Section 13. Factoring Trinomials of the Form + b+ c 4. 3y 4y Objective B Factor out the GCF and then factor a trinomial of the form + b + c y 5y 10y 3 3 Copyright 015 Pearson Education, Inc. 35

6 Developmental Mathematics Third Edition, Elayn Martin-Gay Sec Section 13.3 Factoring Trinomials of the Form a + b + c Complete the outline as you view Lecture Video Pause the video as needed as you fill in all blanks. Circle your answer to each numbered eercise. Then press Play to continue listening to Objective A Factor trinomials of the form a + b+ c where a Objective B Factor out a GCF before factoring a trinomial of the form a + b+ c Copyright 015 Pearson Education, Inc.

7 Developmental Mathematics Third Edition, Elayn Martin-Gay Sec Section 13.4 Factoring Trinomials of the Form a + b + c by Grouping Complete the outline as you view Lecture Video Pause the video as needed as you fill in all blanks. Circle your answer to each numbered eercise. Then press Play to continue listening to Objective A Use the grouping method to factor trinomials of the form a + b+ c To Factor Trinomials by Grouping Step 1: Step : Step 3: Step 4:. 1y + 17y Copyright 015 Pearson Education, Inc. 37

8 Developmental Mathematics Third Edition, Elayn Martin-Gay Sec Section 13.5 Factoring Perfect Square Trinomials and the Difference of Two Squares Complete the outline as you view Lecture Video Pause the video as needed as you fill in all blanks. Circle your answer to each numbered eercise. Then press Play to continue listening to Objective A Recognize perfect square trinomials. Perfect Square Trinomials a + ab+ b a ab+ b Determine whether the trinomial is a perfect square trinomial y + 5y+ 5 Objective B Factor perfect square trinomials. Determine whether the trinomial is a perfect square trinomial. If so, factor y+ 16y 38 Copyright 015 Pearson Education, Inc.

9 Developmental Mathematics Third Edition, Elayn Martin-Gay Sec Section 13.5 Factoring Perfect Square Trinomials and the Difference of Two Squares Objective C Factor the difference of two squares. A contains two terms. Factoring the Difference of Two Squares a b = a+ b a b ( )( ) Factor the difference of two squares m 100n Factor the binomial, if possible r y 9yz m 5 Copyright 015 Pearson Education, Inc. 39

10 Developmental Mathematics Third Edition, Elayn Martin-Gay Sec Section 13.6 Solve Quadratic Equations by Factoring Complete the outline as you view Lecture Video Pause the video as needed as you fill in all blanks. Circle your answer to each numbered eercise. Then press Play to continue listening to Objective A Solve quadratic equations by factoring. Quadratic Equation A quadratic equation is one that can be written in the form a + b + c = 0 where a, b, and c are real numbers and a 0. Zero Factor Theorem If a and b are real numbers, and if ab = 0, then a = 0 or b = 0. Solve the quadratic equation by factoring ( )( ) = 0 To Solve Quadratic Equations by Factoring Step 1: Step : Step 3: Step 4: Step 5: 40 Copyright 015 Pearson Education, Inc.

11 Developmental Mathematics Third Edition, Elayn Martin-Gay Sec Section 13.6 Solve Quadratic Equations by Factoring Solve the quadratic equation by factoring. 3. ( 3 1) = 14 Check: Objective B Solve equations with degree greater than two by factoring. Solve the equation by factoring. 4. ( )( ) = 0 Copyright 015 Pearson Education, Inc. 41

12 Developmental Mathematics Third Edition, Elayn Martin-Gay Sec Section 13.7 Quadratic Equations and Problem Solving Complete the outline as you view Lecture Video Pause the video as needed as you fill in all blanks. Circle your answer to each numbered eercise. Then press Play to continue listening to Objective A Solve problems that can be modeled by quadratic equations. Solve the application problem. 1. The perimeter of the triangle is 85 feet. Find the lengths of its sides.. An object is thrown upward from the top of an eighty-foot building, with an initial velocity of sity-four feet per second. The height, h, of the object after t seconds is given by the quadratic equation h= 16t + 64t+ 80. When will the object hit the ground? Pythagorean Theorem In a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. ( leg) + ( leg) = ( hypotenuse) or a + b = c 4 Copyright 015 Pearson Education, Inc.

13 Developmental Mathematics Third Edition, Elayn Martin-Gay Sec Section 13.7 Quadratic Equations and Problem Solving Solve the application problem. 3. One leg of a right triangle is 4 millimeters longer than the smaller leg and the hypotenuse is 8 millimeters longer than the smaller leg. Find the lengths of the sides of the triangle. 4. The sum of a number and its square is 18. Find the number(s). 5. The product of two consecutive page numbers is 40. Find the page numbers. Copyright 015 Pearson Education, Inc. 43