Polynomials

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Polynomials

• Chapter 5
• SSC 105

2
Greatest Common Factor and Factor By Grouping

• 5.4
• SSC 105

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Why factor?
To solve equations. Thats why!
If a fly ball is hit with a velocity of 60 mph,
how high it goes is modeled by h(t) 88t 16t2.
To find out how long it will take before it hits
the ground, you need to be able to solve the
equation. One method for solving this type of
equation is
Factoring!!
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• To factor a polynomial means to express the
  polynomial as a product of two or more
  polynomials.
• The greatest common factor (GCF) of a polynomial
  is the greatest factor that divides each term of
  the polynomial evenly.

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Factoring opposite of multiplication

• 2x (5x 3) 10x2 6x
• 10x2 6x

GCF
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Factor out the greatest common factor
Identify the GCF 4mn
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Factoring out a negative factor

• Sometimes it is helpful to factor out a negative
  factor, such as the opposite of the GCF. This
  changes the signs of the remaining terms.

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Factoring out a binomial factor
For Exercises 3340, factor out the GCF.
GCF (3z 2b)
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Factoring by Grouping

• mx 3qx my 3qy
• Always try grouping the first two and last two.

mx 3qx my 3qy
Now, factor out a GCF from each grouping
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Factor by Grouping (contd)

• x (m 3q) y (m 3q)

Now, factor out a GCF again!!!
(m 3q)(x y)
Final Answer
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• The order of factors does not matter because
  multiplication is commutative.
• (q 3)(p 7) (p 7) (q 3)
• It is sometimes necessary to rearrange the
  original four terms to factor by grouping.

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Exercise 12

• Factor by grouping
• 5x3 21 35x2 3x 
• A) (5x2 3)(x 7)
• B) 5x3 21 x(35x 3)
• C) (7x2 3)(x 5) 
• D) (5x2 7)(x 3)

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Exercise 10

• What is the greatest common factor of 3z4t3
  15z6t2 9z3t4 ?
• A) 3
• B) 3z3t2
• C) 3z4t3
• D) 15z6t4

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Exercise 11

• Factor out the greatest common factor
• 6t6 8t5 10t3  
• A) 2(3t6 4t5 5t3)
• C) 6t6(8t5 10t3) 
• B) 6t3(t3 t2 2)
• D) 2t3(3t3 4t2 5)