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Factoring Quadratics

Factoring Quadratics. Special Factoring Patterns. Difference of Squares a 2 – b 2 = (a + b)(a – b) Example: x 2 – 36 = (x + 6)(x – 6) a 2 – 49 = (x + 7)(x – 7). Special Factoring Patterns. Perfect Square Trinomial a 2 + 2ab + b 2 = (a + b) 2 a 2 - 2ab + b 2 = (a - b) 2 Example:

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Factoring Quadratics

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  1. Factoring Quadratics

  2. Special Factoring Patterns • Difference of Squares • a2 – b2 = (a + b)(a – b) • Example: • x2 – 36 = (x + 6)(x – 6) • a2 – 49 = (x + 7)(x – 7)

  3. Special Factoring Patterns • Perfect Square Trinomial • a2 + 2ab + b2 = (a + b)2 • a2 - 2ab + b2 = (a - b)2 • Example: • a2 + 8a + 16 = (a + 4)2 • a2 – 10a + 25 = (a - 5)2

  4. X-box Factoring

  5. X-box Factoring • This is a guaranteed method for factoring quadratic equations—no guessing necessary! • We will learn how to factor quadratic equations using the x-box method • Background knowledge needed: • Basic x-solve problems • General form of a quadratic equation • Dividing a polynomial by a monomial using the box method

  6. Standard 11.0 Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. Objective: I can use the x-box method to factor non-prime trinomials.

  7. Factor the x-box way y = ax2 + bx + c GCF GCF Product ac=mn First and Last Coefficients 1st Term Factor n GCF n m Middle Last term Factor m b=m+n Sum GCF

  8. -12 4 Examples Factor using the x-box method. 1. x2 + 4x – 12 a) b) x +6 x26x -2x -12 x 6 -2 -2 Solution: x2 + 4x – 12 = (x + 6)(x - 2)

  9. Examples continued 2. x2 - 9x + 20 a) b) x -4 -4-5 20 -9 x2-4x -5x 20 x -5 Solution: x2 - 9x + 20 =(x - 4)(x - 5)

  10. Guided Practice Grab your worksheets, pens and erasers!

  11. Practice Factor: x2 – 7x +10 (x -5)(x – 2) q2 – 11q +28 (q - 7)(q – 4)

  12. Practice Factor: x2 – 81 (x - 9)(x + 9) q2 – 26q +169 (q - 13)2

  13. Practice Factor: x2 – 49 (x - 7)(x + 7) q2 – 16q + 64 (q - 8)2

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