Write

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Write

• What is a factor of a number? What mathematical
  operation is factoring about?
• What methods for factoring have we discussed?
• What methods for factoring have we discussed?

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Review 3 Factoring Polynomials

• Wednesday 16 January 2008

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Review Week

• Friday Linear Equations
• Monday Systems
• Tuesday Multiplying Polynomials
• Wednesday Factoring Polynomials
• Thursday Solving Quadratics
• And Friday is a half-day.

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The Factors of a Number

• A factor is a number that divides evenly into an
  integer.
• You can also think of it as a multiplication
  ingredient in the number.
• For this reason, they tend to come in pairs.

• 24

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The Fundamental Theorem Of Arithmetic

• Every natural number is either prime or can be
  written as a unique product of prime numbers.
• You can do things in a different order, but its
  the same list of factors, and in the same
  quantity.

• 6,936 22231717
• 1,200 24 3 52

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Greatest Common Factor

• The largest number that is a factor of both.
• Determined by taking as much as you can from the
  prime factorizations of both numbers

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Prime Factors of a Monomial

• 45x3y2

• Same idea except there are variables involved.

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The Greatest Common Factor of two monomials

• Same as GCF of two numbers, except you also have
  to take as many of the variables as you can.

• 12f2g5 20f3g2
• 15r2s7 20r3s5
• 35rs3

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Determine the GCF of these sets of monomials.
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Dividing with Exponents A Rule
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Factoring is the Opposite of Multiplying
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Factoring Using the GCF

• When when the terms of your polynomial have a
  GCF greater than 1.
• How
• 1. Find the GCF.
• 2. Write it outside parentheses.
• 3. Divide each term of the polynomial by the GCF.
• 4. Check by distributing.
• You should get what you started with!

• 3x2 9x

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You Try

• 15x6 - 9x3 12x2

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A Slightly Tougher Example

• 6a5b4 12a3b2 4a8b

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You Try
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But what if the GCF 1?

• x2 7x 12

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A Famous Shortcut
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Factoring
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So to factor

• (x a)(x b) x2 (ab)x ab

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For Example

• x2 7x 10 x2 3x - 4

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Some Generalizations

• x2 4x 3 x2 - 8x 15 x2 - 2x - 35

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ax2 bx c

• When If a ? 1.
• How
• Multiply a by c.
• You need 2 numbers with this product, and a sum
  of b.
• Re -write your equation with these coefficients
  on your just-plain-x term.
• Factor out GCFs.
• Combine to rewrite and finish factoring.

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Try a Few

• x2 4x 3 x2 - 8x 15 x2 - 2x 35

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Factoring

• What are the ideas? What do we need to know?