Lesson #7 Trinomial Factoring

Recall that we have learnt how to factor a polynomial 3 ways so far. 2x3y2 + 4x2y5 – 16x4y3 Common Factoring =2x2y2 (x + 2y3 – 8x2y) 6ab + 3b – 4a - 2 Group Factoring =3b (2a + 1) - 2 (2a + 1) =(a + 1) (3b - 2) (25x2 – 16y2) Difference of Squares Factoring = (5x – 4y) (5x + 4y)

x2 +bx + c There is another way. If it is a trinomial of the form where b and c are integers, we use what we call Munchkin Numbers. Expand using FOIL (x + n)(x + m) =x2 +mx +nx + mn =x2 +(m+n)x + mn b equals the sum of 2 numbers: b = m+n c equals the product of 2 numbers c = mn

eg. 1 Factor these trinomials 1. x2 + 6x + 8 2. x2 + 7x + 12 =(x + )(x + ) 4 2 =(x + )(x + ) 4 3 3. x2 -2x - 15 4. x2 + 7x - 30 =(x - )(x + ) 5 3 =(x - )(x + ) 3 10 5. x2 - 13x + 42 6. a2 -5 ab + 4b2 =(x - )(x - ) 7 6 =(a - )(a - ) 4b b

ax2 +bx + c There is another case for trinomials of the form Again, a, b and c are integers. For these problems, use group factoring. ax2 + bx + c =ax2 +mx +nx + c eg. 2 2x2 + 8x + 6 =2x2 + 6x +2x + 6 =2x(x + 3) +2(x + 3) =(x + 3)(2x+2)

eg. 3 Or use a try and error method 1. 2x2 - 5x + 2 2. 3x2 - 5x - 12 =(2x + )(x + ) 1 4 =(3x + )(x - ) 4 3 3. 6x2 -11x + 4 4. 6x2 -29x - 5 =(3x - )(2x - ) 4 1 =(6x + )(x - ) 1 5

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