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Factoring

Learn to factor polynomials using the GCF, factored form, and special products. Explore examples and solutions to enhance your understanding of polynomial factoring. Practice solving equations efficiently.

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Factoring

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  1. Factoring Chapter 7

  2. Factored Form I can factor polynomials using the GCF.

  3. Factored Form Vocabulary factored form: a polynomial written as a product of factors • greatest common factor (GCF): a monomial that divides evenly into each term

  4. Factored Form • Examples • Write the polynomial in factored form by factoring out the GCF. • #1) 6x2 + 3x • #2) 7z7 + 2z6

  5. Factored Form • Solutions • #1) 3x(2x + 1) • #2) z6(7z + 2)

  6. Factored Form • Examples • Solve the equation. • #3) 6k2 + k = 0 • #4) 7p2 = 21p

  7. Factored Form • Solutions • #3) k(6k + 1) = 0, k = 0, -1/6 • #4) 7p2– 21p = 0, 7p(p – 3) = 0, p = 0, 3

  8. Factoring x2 + bx + c I can factor x2 + bx + c.

  9. Factoring x2 + bx + c Core Concepts In order to factor a trinomial of the form x2 + bx + c, we must find 2 numbers that multiply to be c and add to be b.

  10. Factoring x2 + bx + c Examples Factor. #1) c2 + 8c + 7 #2) x2– 11x + 18

  11. Factoring x2 + bx + c Solutions #1) (c + 7)(c + 1) #2) (x – 9)(x – 2)

  12. Factoring x2 + bx + c • Examples Factor. #3) b2 + 3b - 54 #4) y2– y - 2

  13. Factoring x2 + bx + c Solutions #3) (b + 9)(b – 6) #4) (y - 2)(y + 1)

  14. Factoring x2 + bx + c • Example Solve the equation. #5) g2– 13g + 40 = 0

  15. Factoring x2 + bx + c Solution #5) (g – 8)(g – 5) = 0, g = 8, 5

  16. Factoring ax2 + bx + c I can factor ax2 + bx + c.

  17. Factoring ax2 + bx + c Examples Factor the polynomial. #1) #2)

  18. Factoring ax2 + bx + c Solutions #1) #2)

  19. Factoring Special Products I can factor the difference of 2 squares and factor perfect square trinomials.

  20. Factoring Special Products • Core Concepts • Difference of 2 Squares • a2 - b2 = (a + b)(a - b) Perfect Square Trinomial a2 + 2ab + b2 = (a + b)(a + b) = (a + b)2

  21. Factoring Special Products Examples Factor. • #1) • #2)

  22. Factoring Special Products Solutions #1) #2)

  23. Factoring Special Products • Examples Factor. #3) #4)

  24. Factoring Special Products Solutions #3) #4)

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