Algebra2 Polynomials Factoring

8/13/2019 Algebra2 Polynomials Factoring

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AIM: How do we factor polynomials?

How do we find the zeros of

polynomials?

DO NOW:

1. Find the product of

+

.

**Please have on desk: Yesterdays hw

**Please write down in planner: tonights hw

workbook page 70 #s 1, 2, 5, and pg 71 #1


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DO NOW:

1. Find the product of

+

.


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Homework Review


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Yesterdays Exit Slip


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Factoring Method 1:Factor out the GCF

Step 1: Find the GCF (greatest common factor)

Step 2: Divide the expression by the GCF

Step 3: Write the expression as a produce of theGCF and the quotient

Ex: 5

+ 25

30


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Factoring Method 2: Difference of two

square

Step 1: If there is a GCF, factor out first

Step 2: If you have a binomial in the form

, you factor this as ( + )( )

Step 3: See if you can factor any further

Ex 1: 144 16


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Factoring Method 3: Sum/Product Method

Step 1: If there is a GCF, factor out first.Step 2: If you have trinomial in the form

+ + , you can factor as ( + #)( + #)

where the #s add to b and multiply to cStep 3: See if you can factor any further

Ex 1: Factor 3x2+ 12x + 12


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Method 4: Factoring By Grouping for

Trinomials (I do)

Step 1: If there is a GCF, factor out first.Step 2: If you have a trinomial in the form + +, factor by grouping (steps 3 to 8)

Step 3: Multiply a and c

Step 4: Find #s that multiply to ac and add to bStep 5: Write bx as a sum of #s from Step 4

Step 6: Factor out GCF of first two terms

Step 7: Factor out GCF of last two terms

Step 8: Factor out GCF of whole expression

Ex 1: 3x2+ 11x + 6


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Method 5: Factoring By Grouping for

Polynomial 4 terms (I do)

Step 1: If there is a GCF, factor out first.Step 2: If you have a polynomial with 4 terms,

factor by grouping (steps 3 to 5)

Step 3: Factor out GCF of first two termsStep 4: Factor out GCF of last two terms

Step 5: Factor out GCF of whole expression

Step 6: See if you can factor any further

Ex 1: 8 + 4 18 9


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1. a816

2. y5 + 8y4

3. 2s218

4. 3c3+ 9c2+ 6c

5. j3k4+ 2j2k

6. 2t3+ 4t23t6
http://www.youtube.com/watch?v=OFSrINhfNsQ


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Zeros of Polynomials

Polynomial:

Zeros:


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Zeros on the Graph


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Zeros on the Graph


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We can solve polynomial equations by graphing, or

We can FACTOR!Example 1: Find the zeros of f(x) = 2x4+ 6x3+ 4x2.

2x4+ 6x3+ 4x2= 0

2. Factor out a GCF if possible.

3. Factor more!

4. Set each factor equal

to zero and solve.

1. Set the polynomial equal to zero.


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Example 2: Solve x32x2+ 3x= 6

Factor out a GCF

if possible.

Factor more!

Set each factorequal to zero and

solve.

Set the polynomial

equal to zero.


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Example 3: Solve 8x210x12 = 0

Factor out a GCF

if possible.

Factor more!


solve.

Set the polynomial

equal to zero.


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What if a quadratic is unfactorable?

Ways to solve a quadratic algebraically: 1)

2)

3)

Ex: + 2 5 = 0

P i S l h f ll i


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Practice

Solve the following

equations by factoring:

1. x3+ 2x2= 35x

2. x33x2+ x3= 0

3. 8x2+ 3 = 10x

Factor out a GCF

if possible.

Factor more!


solve.

Set the polynomial

equal to zero.


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Exit Slip

Find the zeros of the following polynomials.

1)

+

= 1

2) = 16

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Algebra2 Polynomials Factoring