FACTORING RULES 1 GCF Greatest Common Factor First

FACTORING RULES 1

*GCF( Greatest Common Factor) – First Rule 4 TERMS Grouping 3 TERMS Perfect Square Trinomial AC Method with Grouping 2 TERMS Difference Of Two Squares Sum or Difference Of Two Cubes 2

GCF Greatest Common Factor First Rule to Always Check 3

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4 TERMS - Grouping 7

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3 TERMS 1) Perfect Square Trinomials 2) 2) AC Method With Grouping We will explore factoring trinomials using the ac method with grouping next and come back to Perfect Square Trinomials later. 9

Factoring Trinomials by Using The AC Method With Grouping 10

Factor the trinomial completely. The first rule of factoring is to factor out the Greatest Common Factor (GCF). 11

Stop! Check that you have factored the (GCF) correctly by distributing it back through the remaining polynomial to obtain the original trinomial. 12

After factoring out the (GCF), the remaining polynomial is of the form To factor , we must find two integers whose product is ac and whose sum is b. To factor , we must find two integers whose product is -60 and whose sum is 7. 13

FACTORS OF SUM OF FACTORS OF 14

ac = b=7 Replace b = 7 in our original expression with b = 12 + (-5). 15

FINISH FACTORING BY GROUPING 16

FACTORED COMPLETELY 17

Practice Problems 18

GCF KEY # FACTORS OF SUM OF FACTORS OF 19

GCF KEY # FACTORS OF SUM OF FACTORS OF 20

GCF KEY # FACTORS OF SUM OF FACTORS OF 21

GCF KEY # FACTORS OF SUM OF FACTORS OF 22

GCF KEY # FACTORS OF SUM OF FACTORS OF 23

GCF KEY # FACTORS OF SUM OF FACTORS OF 24

Answers To Practice Problems 25

Perfect Square Trinomials 26

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2 TERMS 1) Difference of Two Squares 2)2) Sum and Difference of Two Cubes 28

Difference of Two Squares 29

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Sum and Difference of Two Cubes 31

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What purpose does factoring serve? Factoring is an algebraic process which allows us to solve quadratic equations pertaining to real-world applications, such as remodeling a kitchen or building a skyscraper. We will cover the concept of solving quadratic equations and then investigate some realworld applications. 36

Solving Quadratic Equations A quadratic equation is an equation that can be written in standard form where a, b, and c represent real numbers, and 37

We will solve some quadratic equations using factoring and the Zero-Factor Property. When the product of two real numbers is 0, at least one of them is 0. If a and b represent real numbers, and if then a=0 or b=0 38

Solve Each Equation 39

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REAL-WORLD APPLICATIONS USING QUADRATIC EQUATIONS 43

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The height h in feet reached by a dolphin t seconds after breaking the surface of the water is given by h How long will it take the dolphin to jump out of the water and touch the trainer’s hand? 46

From the top of the building a ball is thrown straight up with an initial velocity of 32 feet per second. The equation below gives the height s of the ball t seconds after thrown. Find the maximum height reached by the ball and the time it takes for the ball to hit the ground. 47