1. 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)

2. 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, **
5x2 + 2x + 25x + 10
(5x2 + 2x)+(25x + 10)
x(5x + 2) + 5(5x + 2)
(5x + 2)(x + 5)

3. Example 24x2 – 22x + 3 24*3 = 72 Factors of 72 & sum 1,72 73 2,36 381, 2, 3,
4, **
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!!

4. 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,
-1, 3,
-3,5 2
None add up to 7 so it is PRIME.

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

6. 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 odd, 42, 44, 45