9-5: FACTORING TRINOMIALS OF THE TYPE X 2 + BX + C Essential Question: How do you determine what numbers are used when factoring?

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Presentation transcript:

9-5: FACTORING TRINOMIALS OF THE TYPE X 2 + BX + C Essential Question: How do you determine what numbers are used when factoring?

9-5: Factoring x 2 + bx + c No need to copy  Factoring is FOIL-ing in reverse  To factor a polynomial, you’ll need to know how to find the possible factors of a number  List all of the factors of each number (on board) 

9-5: Factoring x 2 + bx + c  Factoring: The Steps  Make sure the equation is written in standard form f(x) = x 2 + bx + c  Set up two parenthesis ( )( )  Find two numbers with A product of c A sum of b  Write answer as (x ± 1 st number)(x ± 2 nd number)

5-4: Factoring Quadratic Expressions Multiply: + number Multiply: - number Add: + number Add: - number Add: + number Add: - number Both #s are +Both #s are -Bigger # is +Bigger # is - Some hints about finding the two numbers to be used in factoring:

9-5: Factoring x 2 + bx + c  Example #1: Factor x 2 + bx + c  Factor x 2 + 7x + 12 Find the factors of 12. Which pair adds to 7? 1 & 12 2 & 6 3 & 4  Winner, winner x 2 + 7x + 12 = (x + 3)(x + 4)

9-5: Factoring x 2 + bx + c YY OUR T URN FFactor each expression gg 2 + 7g + 10 (g + 5)(g + 2) vv v + 20 (v + 20)(v + 1) aa a + 30 (a + 10)(a + 3)

 Example #2: Factor x 2 – bx + c  Factor d 2 – 17d + 42 Find the factors of 42. Which pair adds to -17? -1 & & & -14  Works -6 & -7 d 2 – 17d + 42 = (d – 3)(d – 14)

9-5: Factoring x 2 + bx + c YY OUR T URN FFactor each expression kk 2 – 10k + 25 (k – 5)(k – 5) xx 2 – 11x + 18 (x – 2)(x – 9) qq 2 – 15q + 36 (q – 12)(q – 3)

 Example #3: Factoring trinomials with a negative c  Factor m 2 + 6m – 27 Find the factors of 27. Which pair adds to 6? Because it adds to a +6, the bigger number is positive -1 & & 9  Got it m 2 + 6m – 27 = (m – 3)(m + 9)  Factor p 2 – 3p – 18 Find the factors of 18. Which pair adds to -3? Because it adds to a -3, the bigger number is negative 1 & & -9 3 & -6  Got it p 2 – 3p – 18 = (p + 3)(p – 6)

9-5: Factoring x 2 + bx + c YY OUR T URN FFactor each expression mm 2 + 8m – 20 (m + 10)(m – 2) pp 2 – 3p – 40 (p – 8)(p + 5) yy 2 – y – 56 (y – 8)(y + 7)

 Assignment  Worksheet #9-5  1 – 27, all