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FACTORING RULES

FACTORING RULES. *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.

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FACTORING RULES

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  1. FACTORING RULES

  2. *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

  3. GCFGreatest Common Factor First Rule toAlwaysCheck

  4. 4 TERMS - Grouping

  5. 3 TERMS • Perfect Square Trinomials • 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.

  6. Factoring Trinomials by Using The AC Method With Grouping

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

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

  9. 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.

  10. FACTORS OF SUM OF FACTORS OF

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

  12. FINISH FACTORING BY GROUPING

  13. FACTORED COMPLETELY

  14. Practice Problems

  15. GCF KEY # FACTORS OF SUM OF FACTORS OF

  16. GCF KEY # FACTORS OF SUM OF FACTORS OF

  17. GCF KEY # FACTORS OF SUM OF FACTORS OF

  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. Answers To Practice Problems

  22. Perfect Square Trinomials

  23. 2 TERMS • Difference of Two Squares • 2) Sum and Difference of Two Cubes

  24. Difference of Two Squares

  25. Sum and Difference of Two Cubes

  26. 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 real-world applications.

  27. 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

  28. 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

  29. Solve Each Equation

  30. REAL-WORLD APPLICATIONS USING QUADRATIC EQUATIONS

  31. 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?

  32. 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.

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