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Factoring Trinomials

Factoring Trinomials. Review: (y + 2)(y + 4) Multiply using FOIL. FOIL: Combine like terms. y ² + 4y + 2y + 8 = y ² + 6y + 8 y² + ( 4+2 )y + ( 4*2 ). x 2 + bx + c. y² + 6y + 8 y² + ( 4+2 )y + ( 4*2 )

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Factoring Trinomials

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  1. Factoring Trinomials

  2. Review: (y + 2)(y + 4)Multiply using FOIL. FOIL: Combine like terms. y² + 4y + 2y + 8 = y² + 6y + 8 y² + (4+2)y + (4*2)

  3. x2 + bx + c y² + 6y + 8 y² + (4+2)y + (4*2) *To factor, you have to find the factors of c that add to = b. = (x + 4)(x + 2)

  4. x2 + bx + c x2 + bx + c x2 - bx + c (x+p)(x+q) (x-p)(x-q) x2 + bx – c x2 – bx - c (x+p)(x-q) (x-p)(x+q) * If p and q are factors of ac that add to = b and p > q.

  5. 1) Factor. y2 + 6y + 8 Create a table as shown below. Factors of: Multiply the 1st and last coefficients. Sum of: Middle Term Factors of +8 Sum of +6

  6. 1) Factor. y2 + 6y + 8 F +8 S +6 +1, +8 +2, +4 Place the factors in the table.

  7. +9, NO +6, YES 1) Factor. y2 + 6y + 8 Which box has a sum of +6? F +8 S +6+1, +8 +2, +4 y Answer: (y + 2)(y + 4) y

  8. 2) Factor. x2 - 2x - 63Put the factors and sum into the table, list the factors, and determine which one is correct. F -63 S -2+1, -63+3, -21 +7, -9 -2, YES Answer: (x+7)(x-9)

  9. 3) Factor. -c2 + 20c - 100 • You always want your a positive in ax2 + bx + c *So we need to factor out a -1 to make a = +1. -1(c2 - 20c +100)

  10. -1(c2 - 20c +100) • F 100 S -20-1, -100 -2, -50 -4, -25-5, -20 -10, -10 -10 + -10 = -20 = -(c -10)(c-10)

  11. 4) Factor: -y2 - 6y + 55 Answer: -(y+11)(y-5) 5) Factor: a2 – 5a + 4 Answer: (a-4)(a-1) 6) Factor: -4s2 - 40s - 84 Answer: -4(s+7)(s+3)

  12. Solve the equation: x2 - 3x - 40 = 0 F -40 S -3 +1, -40 +2, -20 +4, -10 +5, -8 -3 -yes So, (x+5)(x-8)=0 x+5 = 0 or x-8 =0 x = -5 or x = 8

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