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5.6 Factoring Trinomials

5.6 Factoring Trinomials. How to Factor. 1. Write the trinomial in descending powers of one variable. 2. Factor out any GCF (including (-1) to make the 1 st term positive) 3. Test the trinomial for factorability. Check the value of

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5.6 Factoring Trinomials

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  1. 5.6 Factoring Trinomials

  2. How to Factor • 1. Write the trinomial in descending powers of one variable. • 2. Factor out any GCF (including (-1) to make the 1st term positive) • 3. Test the trinomial for factorability. • Check the value of • If it’s a perfect square, then it’s factorable into 2 different binomials • If it’s zero, then it’s factorable and the factors will be the same

  3. More steps • 4. When the sign of the 1st term of the trinomial is positive: • And the sign of the 3rd term is positive, the signs in each parentheses will be the same • And the sign of the 3rd term is negative, the signs in each parentheses will be different

  4. More steps continued • 5. Try different combos until you find the one that works. • If the leading coefficient is 1 • Pick the factorization where the sum of the factors of c is equal to the coefficient of the middle term (b) • If the leading coefficient is not 1 • Can use trial and error • Can use the key method

  5. Step 5 Cont’d (Key Method) • i. Find product of ac (this is the key #) • ii. Find 2 factors of the key # whose sum is b • iii. Use the factors of the key # as coefficient of 2 terms to be placed between • iv. Factor using grouping

  6. Example of key method • 6. Check by multiplying out.

  7. Another example – key method

  8. Using Substitution to Factor

  9. Using Grouping to Factor Trinomials

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