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Factoring Quadratic Trinomials Lesson

Learn how to factor quadratic trinomials of the form ax^2 + bx + c using Box and Diamond and Guess and Check methods.

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Factoring Quadratic Trinomials Lesson

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  1. Lesson Objective:I will be able to … • Factor quadratic trinomials of the form • ax2 + bx + c • Language Objective: I will be able to … • Read, write, and listen about vocabulary, key • concepts, and examples

  2. Page 15

  3. Example 1: Factoring ax2 + bx + c by Box and Diamond Page 16 Factor 6x2 + 11x + 4 by box and diamond. 6x2 + 11x + 4 24x2 6x2 ● 4 = 24x2 1 3x 4 3x 8x 2x 6x2 8x 11x 3x 4 Use the Generic Rectangle to factor the trinomial. Step 1 Factor out the GCF from first column. Step 2 3x ● ? = 6x2 Step 3 2x ● ? = 8x Step 4 4 ● ? = 4 6x2 + 11x + 4 = (2x + 1)(3x + 4)

  4. Product = c Product = a Sum of outer and inner products = b To factor a2 + bx + c, check the factors of a and the factors of c in the binomials. The sum of the products of the outer and inner terms should be b. ( X + )( x + ) =ax2+bx+c

  5. ( x + )( x + ) Factors of 3 Factors of 16Outer+Inner  = 3x2 – 16x + 16 Example 2: Factoring ax2 + bx + c by Guess and Check Page 17 Factor 3x2 – 16x + 16. Check your answer. a = 3 and c = 16, Outer + Inner = –16.  1 and 3 –1 and –16 1(–16) + 3(–1) = –19  1( – 8) + 3(–2) = –14 1 and 3 – 2 and – 8  – 4 and – 4 1( – 4) + 3(– 4)= –16 1 and 3 (x – 4)(3x – 4) Use the Foil method. Check(x – 4)(3x – 4) = 3x2 – 4x – 12x + 16

  6. Example 3: Factoring ax2 + bx + c with Negatives Page 18 Factor 3n2 + 11n – 4. Check your answer. 3n2 + 11n– 4 -12n2 3n2 ● -4 = -12n2 4 12n -4 12n -n n 3n2 -n 11n 3n -1 Use the Generic Rectangle to factor the trinomial. Step 1 Factor out the GCF from first column. Step 2 3n ● ? = 3n2 Step 3 n ● ? = -n Step 4 -1 ● ? = -4 3x2 + 11x – 4 = (n + 4)(3n – 1)

  7. Caution When you factor out –1 in an early step, you must carry it through the rest of the steps. When the leading coefficient is negative, factor out –1 from each term before using other factoring methods.

  8. –1( x + )( x+ ) Factors of 2 Factors of 3Outer+Inner (x + 1)(2x + 3) Example 4: Factoring ax2 + bx + c When a is Negative Page 19 Factor –2x2 – 5x – 3. –1(2x2 + 5x + 3) Factor out –1. a = 2 and c = 3; Outer + Inner = 5  1 and 2 3 and1 1(1) + 3(2) = 7  1 and 3 1 and 2 1(3)+ 1(2) = 5 –1(x + 1)(2x + 3), or –(x + 1)(2x + 3)

  9. Chapter 8 Quick Review Assignment #14 1. Write the prime factorization of 48. 2. Factor out the GCF: 18x2y4 – 27xy3 3. Factor: x2 – 6x + 8 4. Factor: 3n2 + 16n + 21

  10. Classwork • Chapter 8 Quiz

  11. Homework Assignment #14 • Holt 8-4 #36, 39, 42, 45, 48, 51, 54, 67, 68, 70, 77 – 82 • Holt 8-3 #33 – 36, 38 – 43 • KIN 8-5

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