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“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.

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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

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Click on the size of your polynomial

Binomial

Trinomial

Four Terms

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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)

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Factoring 4 terms

• Factor by “Grouping”

• After factor by “Grouping” Click_Here

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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

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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

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Can you factor out a common factor?

Yes

No

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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)

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Can you factor out a common factor?

Yes

No

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Is it a “Perfect Square Trinomial”?

Yes

No

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“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)²A²-2AB+B²= (A-B)²Example:x²+ 6x +9 = (x+3)²

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• Use “Bottom’s Up” to factor

• After “Bottoming Up”

Factoring Trinomials Using “Bottom’s Up”

Click_Here

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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

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“Bottom’s Up”Ex: 2x² – 7x -4

• 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

Mult. First and last terms

2(-4)=-8

Write the middle term

-7

-8

-7

-81

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“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)

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Can you factor out a common factor?

Yes

No

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Is it the “Difference of Two Squares”?

Yes

No

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“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)

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

is it another “Difference of Two Squares”?

Yes

No

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

is it another “Difference of Two Squares”?

Yes

No

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Congratulations

You have completely factored your polynomial! Good Job!

Click on the home button to start the next problem!

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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.