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FACTORING RULES

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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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Presentation Transcript
slide2
*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

slide9
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.

slide10
Factoring Trinomials

by

Using The

AC Method

With

Grouping

slide11
Factor the trinomial completely.

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

slide12
Stop! Check that you have factored the (GCF)correctly by distributing it back through the remaining polynomial to obtain the original trinomial.
slide13
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.

slide14
FACTORS OF

SUM OF FACTORS OF

slide15
ac = b = 7

Replace b = 7 in our original expression with

b = 12 + (-5).

slide19
GCF

KEY #

FACTORS OF

SUM OF FACTORS OF

slide20
GCF

KEY #

FACTORS OF

SUM OF FACTORS OF

slide21
GCF

KEY #

FACTORS OF

SUM OF FACTORS OF

slide22
GCF

KEY #

FACTORS OF

SUM OF FACTORS OF

slide23
GCF

KEY #

FACTORS OF

SUM OF FACTORS OF

slide24
GCF

KEY #

FACTORS OF

SUM OF FACTORS OF

slide28
2 TERMS
  • Difference of Two Squares
  • 2) Sum and Difference of Two Cubes
slide36
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.

slide37
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

slide38
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

slide43
REAL-WORLD

APPLICATIONS

USING

QUADRATIC

EQUATIONS

slide46
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?

slide47
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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