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Unit 2: Expressions and Polynomials

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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Unit 2: Expressions and Polynomials

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  1. Unit 2: Expressions and Polynomials GCF and Factoring

  2. 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

  3. GCF and Factoring • Factor the GCF out of the following polynomial

  4. Factoring Polynomials • Review:

  5. Factoring Polynomials Bottoms Up! • To factor polynomials in the form • Use the Bottoms Up Method • This method works for factoring any type of polynomial!

  6. 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

  7. 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)

  8. 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)

  9. 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

  10. Try! • Factor the following: • 1) • 2)

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