Unit 3Factoring by GCF

Algebra 1

How do I get ready for class? 1) On Desk: binder, pens/pencils2) You are tardy if you are not in your seat when the bell rings

Homework: Factoring by GCF

Upcoming……Quiz Today!

Warm Up: What is the greatest common factor of 16 and 24?

Standards

MGSE9–12.A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

MGSE9–12.A.SSE.3a Factor any quadratic expression to reveal the zeros of the function defined by the expression.

What do you already know about

these standards?

Learning Goal • Students will be able to factor a quadratic expression

to solve a real world problem.

Where are you on the Learning Scale?

Scale Rubric # of students

4 I can create a model for a real world problem using quadratic functions andteach a peer.

3 I can factor a quadratic expression to solve a real world problem. (ax2 + bx + c)

2 I can factor polynomials completely by using the GCF and grouping.

1 I can recognize factors and find the GCF or monomials.

Factors and Greatest Common Factor (GCF)

Vocabulary

Factors

• Numbers, variables, or polynomials that are multiplied to find a product.

Example: What are the factors of 24?

Vocabulary

Greatest Common Factor

• The greatest factor shared by two or more numbers, variables or polynomials.

Example: What is the greatest common factor of 12 and 32?

Finding the GCF of Numbers

Find the GCF of each pair of terms.

1) 100 and 60

GCF of Monomials

Find the GCF of each pair of monomials.

15x3 and 9x2

GCF of Monomials

Find the GCF of the monomials.

9a2b2, 6ab3, and 12b

GCF of Monomials

Find the GCF of each pair of monomials.

8x2 and 7y3

GCF of Expressions with Binomial Factors

Find the GCF of the expressions.

6(x-2)3 and 8(x-2)4

GCF of Expressions with Binomial Factors

Find the GCF of the expressions.

2y(x - 4)5 and 8y2(x - 4)

Factoring by GCF

Factoring Polynomials

What is the GCF of 15x2 and 20x ?

How would you factor 15x2 + 20x using the GCF?

Factoring Polynomials

1. Write the polynomial under the upside down division sign.

2. Find the greatest common factor of all the terms.

3. Place the GCF on the outside and divide (“factor out”) each term by the GCF.

Factoring Polynomials

4. After “factoring out” the GCF, the only that number that divides into each term should be 1.

5. Place parentheses around the terms at the bottom of the division sign.

6. Write your answer with the GCF outside of the parentheses.

Factoring BY GCF

Factor the polynomials using the GCF.

1) x2 + 4x GCF =

2) b2 - 5b GCF =

Factoring BY GCF

Factor the polynomials using the GCF.3) -2y2 - 6y GCF =

4) 32x4 - 16x3 + 8x2 GCF =

Factoring BY GCF

Factor the polynomials using the GCF.

5) 3x3 + 2x2 – 10 GCF =

Agenda

• Homework Review: Evaluating Functions

• Quiz – Factoring

• Homework for Today: Factoring by GCF