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Trinomials

Trinomials

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Pst2 Pst2 Presentation Transcript

  • Perfect Square Trinomial
  • Factoring: Perfect Square TrinomialsThe first criteria of aPerfect Square Trinomialis that it must have threeterms.
  • Using FOIL we find the productof two binomials. (a + b)(a + b) = a + ab + ab + b 2 2 = a + 2ab + b 2 2
  • Rewrite the perfect square trinomial as a binomial squared.So when you recognize this… a + 2ab + b = (a + b)(a + b) 2 2 = ( a + b) 2 …you can write this.
  • Recognizing a Perfect Square Trinomial x + 10 x + 25 2• First term must be a perfect square. (x)(x) = x2• Last term must be a perfect square. (5)(5) = 25• Middle term must be twice the product of the square root coefficient of the first and last term. (2)(5)(1) = 10
  • What if it is a Perfect Square Trinomial x + 10 x + 25 2• If you have a perfect Square Trinomial it is easy to factor:  Take the square root of the first term.  Take the square root of the last term.  Use the sign of the middle term, put in parenthesis and square the result. x + 10 x + 25 = ( x + 5) 2 2
  • Recognizing a Perfect Square Trinomial m + 8m + 16 = (m + 4) 2 2• First term must be a perfect square. (m)(m) = m2• Last term must be a perfect square. (4)(4) = 16• Middle term must be twice the product of the square root coefficient of the first and last term. (2)(4)(1) = 8
  • Recognizing a Perfect Square Trinomial p − 18 p + 81= ( p − 9) 2 2• First term must be a perfect square. (p)(p) = p2• Last term must be a perfect square. Signs must match! (9)(9) = 81• Middle term must be twice the product of the coefficient of the first and last term. (2)(9)(1) = 18p
  • Recognizing a Perfect Square Trinomial Not a Perfect121 p + 110 p + 100 2 Square • First term must be a perfect square. 2 Trinomial! (11p)(11p) = 121p • Last term must be a perfect square. (10)(10) = 100 • Middle term must be twice the product of the first and last term. (2)(10)(11p) = 220p
  • Perfect Square Trinomial Y/N r − 8r + 16 Yes ( r − 4) 2 2 49 p − 28 p + 4 Yes ( 7 p − 2) 2 249 s − 42 st + 36t No 2 2 4m + 4mn + n Yes ( 2m + n ) 2 2 2 d + 50d + 225 No 2
  • HOMEWORK (1/2 CROSSWISE)• Factor x2 + 6x + 9• Factor y – 16y + 64 2• Factor m2 – 12m + 36• Factor 4p + 4p + 1 2• Factor 9k + 12k + 4 2
  • It has the form ofax + bx + c 2
  • E xample• x + 5x + 6 2• x - 2x + 8 2• x + 8x + 16 2