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Factoring

Factoring. Greatest Common Factor The largest common factor in all the terms of the polynomial. Example. pg. 342, # 9. Factoring by Grouping See page 341. Example. Factor: (mx +3qx+my+3qy) We will take the terms in pairs The GCF of mx and 3qx is x The GCF of my and 3qy is y.

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Factoring

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  1. Factoring Greatest Common Factor The largest common factor in all the terms of the polynomial

  2. Example • pg. 342, # 9

  3. Factoring by GroupingSee page 341

  4. Example • Factor: (mx +3qx+my+3qy) • We will take the terms in pairs • The GCF of mx and 3qx is x • The GCF of my and 3qy is y

  5. Example 39 on page 342 • Factor: mx +3qx+my+3qy • Step 1: Use GCF in pairs: x(m+3q) + y( m+3q) • Step 2: Notice or look for any common factors • x(m+3q) + y( m+3q) • Step 3: Factoring out the common factors yields • The factored form is: (m+3q)(x+y)

  6. Special Factorizations

  7. Strategy forFactoring Polynomials

  8. Solving Equations by Factoring

  9. Solve the equation:See page 366 # 18

  10. The Plan • Distribute (FOIL) the left hand side (LHS) • Distribute the right hand side (RHS) • Gather all terms on the RHS, setting the LHS equal to 0 • Factor ( if possible) the LHS • Apply the Zero-Factor Property to Solve (see page 360) • Check our solution in the ORIGINAL Problem

  11. Distribute on RHS and LHS

  12. Gather all terms on the LHS, setting the RHS equal to 0

  13. Remember that we must use trial and error to find the factors until we exhaust all possibilities Factor ( if possible) the LHS

  14. Apply the Zero-Factor Property to Solve

  15. The Check

  16. The Check continued

  17. Solving a Quadratic Equation by Factoring Overview • Step 1: Use algebraic properties to ensure that one side is equal to 0 • Step 2: Factor this polynomial • Step 3: Use the zero-factor property by setting each of the factors equal to 0 • Step 4: Solve each of the equations from step 3 independently • Step 5: Check solution in the original problem

  18. Good Luck! • Only three chapters away from completing the course.

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