Practice Factor each polynomial 1. 3y2 + 2y + 9y + 6 2. 2p2 – 6p + 7p – 21 3. 3a2 + 2a + 12a + 8 4. 3b2 + 7b – 12b – 28 5. 4x2 + 3x + 8x + 6 Answers 1. (y + 3)(3y + 2) 2. (2p + 7)(p – 3) 3. (a + 4)(3a + 2) 4. (b – 4)(3b + 7) 5. (x + 2)(4x + 3)

8.4 Factoring Trinomials: ax2 + bx + c Step 1: Multiply a and c. Step 2: Find the factors of ac. And what those factors add up to… Step 3: Pick the pair that totals b. Step 4: Rewrite the equation in ax2 + mx + nx + c form (where m and n are the factors) Step 5: Factor by grouping and simplify 5x2 + 27x + 10 5*10 = 50 Factors of 50 & sum 1,50 51 2,25 27 ** 5x2 + 2x + 25x + 10 (5x2 + 2x)+(25x + 10) x(5x + 2) + 5(5x + 2) (5x + 2)(x + 5)

Example 24x2 – 22x + 3 24*3 = 72 Factors of 72 & sum 1,72 73 2,36 38 1,72 73 2,36 38 3,24 27 4,18 22** 24x2 – 18x – 4x + 3 24x2 – 18x – 4x + 3 (24x2 – 18x) + (-4x + 3) 6x(4x – 3) – 1 (4x – 3) (4x – 3) (6x – 1) Sometimes they all have something in common so take the GCF out to make it easier!!

Example 4x2 + 24x + 32 Have 4 in common (4 is the GCF) 4(x2 + 6x + 8) Now factor! 4(x + 2)(x + 4) 3x2 + 7x – 5 3*-5 = -15 Factors of 15 & sum 1,-15 -14 -1,15 14 3,-5 -2 -3,5 2 None add up to 7 so it is PRIME.

More Examples 15b2 – 20b + 6b – 8 = 0 (15b2 – 20b)+(6b – 8) = 0 15*-8 = -120 Factors of 120 & sum (sum of -14) 1,-120 -119 -1,120 119 2,-60 -58 -2,60 58 3,-40 -37 -3,40 37 4,-30 -26 -4,30 26 5,-24 -19 -5,24 19 6,-20 -14*Finally 15b2 – 20b + 6b – 8 = 0 (15b2 – 20b)+(6b – 8) = 0 5b(3b – 4)+2(3b – 4) = 0 (5b + 2)(3b – 4) = 0 (5b + 2) = 0 (3b – 4)=0 5b = -2 3b = 4 b = -2/5 b = 4/3 {-2/5, 4/3}

Try These: p. 444 1-9 1. (3a + 2)(a + 2) 2. Prime 3. 2(p + 3) (p + 4) 4. (x + 4)(2x + 5) 5. 3(2x + 1)(x + 3) 6. (2n + 5)(2n – 7) 7. {-3,-2/3} 8. {1/2,7/5} 9.{-5/2, 4/3} Homework #59 p. 445 11-37 odd, 42, 44, 45