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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


*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


Gcf greatest common factor first rule to always check
GCFGreatest Common Factor First Rule toAlwaysCheck



  • 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.


Factoring Trinomials

by

Using The

AC Method

With

Grouping


Factor the trinomial completely.

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


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


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.


FACTORS OF

SUM OF FACTORS OF


ac = b = 7

Replace b = 7 in our original expression with

b = 12 + (-5).





GCF

KEY #

FACTORS OF

SUM OF FACTORS OF


GCF

KEY #

FACTORS OF

SUM OF FACTORS OF


GCF

KEY #

FACTORS OF

SUM OF FACTORS OF


GCF

KEY #

FACTORS OF

SUM OF FACTORS OF


GCF

KEY #

FACTORS OF

SUM OF FACTORS OF


GCF

KEY #

FACTORS OF

SUM OF FACTORS OF




2 TERMS

  • Difference of Two Squares

  • 2) Sum and Difference of Two Cubes




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.


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


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



REAL-WORLD

APPLICATIONS

USING

QUADRATIC

EQUATIONS


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?


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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