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F ACTORING P OLYNOMIALS

Learn how to factor polynomials efficiently with examples and exercises. Understand GCF, difference of squares, and sum/difference of cubes methods. Practice and boost your skills!

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F ACTORING P OLYNOMIALS

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  1. FACTORING POLYNOMIALS FACTORING POLYNOMIALS FACTORING POLYNOMIALS FACTORING POLYNOMIALS SECTION R-5 R-5: Factoring Polynomials

  2. GCF • Find the GCF of 28 and 40 R-5: Factoring Polynomials

  3. GCF • Find the GCF of 2, 7, 5 R-5: Factoring Polynomials

  4. GCF • Find the GCF of x3, x7, x5 R-5: Factoring Polynomials

  5. STEPS IN FACTORING POLYNOMIALS • Determine if there is a GCF in the polynomial. • If there is, divide the whole equation by the GCF. • Put aside the GCF and focus on the factored equation • Factor out the polynomial (put in parentheses) • Write the GCF and polynomials factors together. R-5: Factoring Polynomials

  6. EXAMPLE 1 • Factor out R-5: Factoring Polynomials

  7. EXAMPLE 2 • Factor out R-5: Factoring Polynomials

  8. EXAMPLE 3 • Factor out R-5: Factoring Polynomials

  9. EXAMPLE 4 • Factor out This is known as DIFFERENCE of SQUARES! DIFFERENCE means subtraction…this only works when there is a minus sign. R-5: Factoring Polynomials

  10. EXAMPLE 5 • Factor out 9x2– 16 (3x + 4)(3x– 4) R-5: Factoring Polynomials

  11. Your Turn • Factor out R-5: Factoring Polynomials

  12. EXAMPLE 6 • Factor out R-5: Factoring Polynomials

  13. EXAMPLE 7 • Factor out R-5: Factoring Polynomials

  14. EXAMPLE 8 • Factor out R-5: Factoring Polynomials

  15. Your Turn • Factor out R-5: Factoring Polynomials

  16. Sum/Difference of Cubes x3 – 1 Step 1: Take the cubed root of the front term and back term. Place these in parentheses. Step 2: Take the remaining factors and place them in the front and back term positions. Leave the middle spot open. Step 3: Multiply the cubed roots by each other. Change the sign. This is your middle term.

  17. Sum/Difference of Cubes • 27x3 + 8

  18. Your Turn! • 8x3 – 1 (2x – 1)(4x2 + 2x + 1)

  19. ASSIGNMENT • Pg 51: #5 – 21 odd (skip 9) & #33 – 37 odd R-5: Factoring Polynomials

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