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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

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Factoring rules

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


Gcf greatest common factor first rule to always check

GCFGreatest Common Factor First Rule toAlwaysCheck


Factoring rules

4 TERMS - Grouping


Factoring rules

  • 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 rules

Factoring Trinomials

by

Using The

AC Method

With

Grouping


Factoring rules

Factor the trinomial completely.

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


Factoring rules

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


Factoring rules

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.


Factoring rules

FACTORS OF

SUM OF FACTORS OF


Factoring rules

ac = b = 7

Replace b = 7 in our original expression with

b = 12 + (-5).


Factoring rules

FINISH FACTORING BY GROUPING


Factoring rules

FACTORED COMPLETELY


Factoring rules

Practice Problems


Factoring rules

GCF

KEY #

FACTORS OF

SUM OF FACTORS OF


Factoring rules

GCF

KEY #

FACTORS OF

SUM OF FACTORS OF


Factoring rules

GCF

KEY #

FACTORS OF

SUM OF FACTORS OF


Factoring rules

GCF

KEY #

FACTORS OF

SUM OF FACTORS OF


Factoring rules

GCF

KEY #

FACTORS OF

SUM OF FACTORS OF


Factoring rules

GCF

KEY #

FACTORS OF

SUM OF FACTORS OF


Factoring rules

Answers To Practice Problems


Factoring rules

Perfect Square Trinomials


Factoring rules

2 TERMS

  • Difference of Two Squares

  • 2) Sum and Difference of Two Cubes


Factoring rules

Difference of Two Squares


Factoring rules

Sum and Difference of Two Cubes


Factoring rules

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.


Factoring rules

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


Factoring rules

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


Factoring rules

Solve Each Equation


Factoring rules

REAL-WORLD

APPLICATIONS

USING

QUADRATIC

EQUATIONS


Factoring rules

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?


Factoring rules

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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