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Unit 2: Expressions and Polynomials. GCF and Factoring. GCF. Greatest Common Factor The largest factor in common between two numbers Ex: The GCF between 25 and 30 is 5 Ex: The GCF between 4x and 10 is 2 Ex: The GCF between 5mnp and 15mp is 5mp. GCF and Factoring.

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Presentation Transcript
slide2
GCF
  • Greatest Common Factor
    • The largest factor in common between two numbers
    • Ex: The GCF between 25 and 30 is 5
    • Ex: The GCF between 4x and 10 is 2
    • Ex: The GCF between 5mnp and 15mp is 5mp
gcf and factoring
GCF and Factoring
  • Factor the GCF out of the following polynomial
factoring polynomials bottoms up
Factoring Polynomials Bottoms Up!
  • To factor polynomials in the form
  • Use the Bottoms Up Method
    • This method works for factoring any type of polynomial!
bottoms up steps
Bottoms Up! Steps
  • Step 1: Multiply a and c together
  • Step 2: Find 2 number that multiply to give (ac) and add to give b
  • Step 3: Place each of those numbers inside of separate binomials with x at the beginning
  • Step 4: Divide each of the constants by a
  • Step 5: If any constant is in fraction form, multiply each term in that binomial by the denominator
factoring polynomials bottoms up1
Factoring Polynomials: Bottoms Up!
  • Example:
    • Factor
      • Step 1: Multiply a and c together
        • 1 x 45 = 45
      • Step 2: Two numbers that multiply to give 45 and add to give 14
        • 9 and 5
      • Step 3: Place each number inside of binomials
        • (x + 9) (x + 5)
      • Step 4: Divide each of the constants by a
        • a equals 1, so there is no need to divide further.
      • Your answer is (x + 9)(x + 5)
factoring polynomials bottoms up2
Factoring Polynomials: Bottoms Up!
  • Factor the following polynomial:
    • Step 1: Multiply a and c together
        • 2 x 18 = 36
    • Step 2: Two numbers that multiply to give 36 and add to give 15
        • 12 and 3
    • Step 3: Place each number inside of binomials
        • (x + 12) (x + 3)
factoring polynomials bottoms up3
Factoring Polynomials: Bottoms Up!
    • Step 4: Divide each of the constants by
    • Step 5: Since is not an integer, multiply the 2nd binomial by 2 to get rid of the fraction.
  • Your final answer is
slide10
Try!
  • Factor the following:
    • 1)
    • 2)