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“The Walk Through Factorer”. Ms. Trout’s 8 th Grade Algebra 1 Resources: Smith, S. A., Charles, R. I., Dossey, J.A., et al. Algebra 1 California Edition. New Jersey: Prentice- Hall Inc., 2001. Directions:.

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The walk through factorer

“The Walk Through Factorer”

Ms. Trout’s

8th Grade Algebra 1

Resources:

Smith, S. A., Charles, R. I., Dossey, J.A., et al. Algebra

1 California Edition. New Jersey: Prentice- Hall Inc., 2001.


Directions
Directions:

  • As you work on your factoring problem, answer the questions and do the operation

  • These questions will guide you through

    each problem

  • If you forget what a term is or need an

    example click on the question mark

  • The arrow keys will help navigate you through


Click on the size of your polynomial
Click on the size of your polynomial

Binomial

Trinomial

Four Terms


4 terms factor by grouping ex 6x 9x 4x 6
4 Terms: Factor by “Grouping”Ex: 6x³ -9x² +4x - 6

  • Group (put parenthesis) around the first two terms and the last two terms

    (6x³ -9x²) +(4x – 6)

  • Factor out the common factor from each binomial

    3x²(2x-3) + 2(2x-3)

  • You should get the same expression

    in your parenthesis.

  • Factor the same expression out and

    write what you have left

    (2x-3)(3x² +2)


Factoring 4 terms
Factoring 4 terms

  • Factor by “Grouping”

  • After factor by “Grouping”

Click_Here


Factoring completely
Factoring Completely

  • After factor by “Grouping” check to see if your binomials are the “Difference of

    Two Squares”

  • Are you binomials the “Difference of Two Squares”?

Yes

No


How do you determine the size of a polynomial
How do you determine the size of a polynomial?

  • The amount of terms is the size of the polynomial.

  • The terms are in between addition signs (after turning all subtraction into addition)

  • Binomial has 2 terms

  • Trinomial has 3 terms



How can you tell if you can factor out a common factor
How can you tell if you can factor out a common factor?

  • If all the terms are divisible by the same number you can factor that number out.

  • Example:

    3x² + 12 x + 9

    Hint: (All the terms have a common factor of 3)

    3 (x² +4x +3)



Is it a perfect square trinomial
Is it a “Perfect Square Trinomial”?

Yes

No


Perfect square trinomial
Perfect Square Trinomial”

Criteria:

  • Two of the terms must be squares (A² & B²)

  • There must be no minus sign before the A² or B²

  • If we multiply 2(A)(B) we get the middle term (The middle term can be – or +)

    Rule:

    A² +2AB+B² = (A+B)²

    A²-2AB+B²= (A-B)²

    Example:

    x²+ 6x +9 = (x+3)²


Factoring trinomials using bottom s up
Factoring Trinomials Using “Bottom’s Up”

  • Use “Bottom’s Up” to factor

  • After “Bottoming Up”

Click_Here


Factoring completely1
Factoring Completely

  • After you factor using “Bottom’s Up”, check to see if your binomials are the “Difference of Two Squares”.

  • Are your binomials a “Difference of Two Squares”?

Yes

No


Bottom s up ex 2x 7x 4
“Bottom’s Up”Ex: 2x² – 7x -4

Mult. First and last terms

2(-4)=-8

  • Make your x and label

    North and South

  • Think of the factors that multiply to the

    North and add to the South and

    write those two numbers in the East

    and West

Write the middle term

-7

-8

1

-8

-7


Bottoms up continued ex 2x 7x 4
“Bottoms Up” continued…Ex: 2x² – 7x -4

  • Make a binomial of your east and west

    (x+1) (x-8)

  • Divide by your leading coefficient

    (the number in front of x²)

    (x+1/2) (x-8/2)

  • Simplify the fraction to a whole

    number if you can and if it is still a fraction bring the bottom number up in front of the x

    (2x +1)(x-4)



Is it the difference of two squares
Is it the “Difference of Two Squares”?

Yes

No


Difference of two squares
Difference of Two Squares”

Criteria:

  • Has to be a binomial with a subtraction sign

  • The two terms have to be perfect squares.

    Rule:

    (a²-b²) = (a+b) (a-b)

    Example:

    (x² -4) = (x +2) (x-2)


After factoring using the “Difference of Two Squares” look inside your ( ) again, is it another “Difference of Two Squares”?

Yes

No


After factoring using the “Difference of Two Squares” look inside your ( ) again, is it another “Difference of Two Squares”?

Yes

No


Congratulations
Congratulations

You have completely factored your polynomial! Good Job!

Click on the home button to start the next problem!


Keep continuing to factor the “Difference of Two Squares” until you do not have any more “Difference of Two Squares”. Then you have factored the problem completely and can return home and start your next problem.


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