1. Factoring Trinomials
Bustin’ da B
ax2 + bx + c

2. What 2 numbers when multiplied together give you 24,and when added give you -14?

3. ax2 + bx + c Multiply a and c together, place that value here
Place the b value here
Then ask, what 2 numbers when multiplied together give you a times c, when added give you b?
Place the answers to your question here.

4. Ex. 2x2+10x+12
a times c =24
b = 10
What 2 numbers when multiplied together give you 24,and when added give you 10?
4 and 6 24 6 4 10

5. Fill out the cross for these 4 examples
10x2 + 27x + 5
14x2 + 16x + 2
6x2 + 17x + 7
3x2 + 25x + 8

6. Use these results to bust da b.24 6 4 10
ax2 + bx + c
2x2+10x b= 10 or 4 + 6
4 and 6 were my previous results
So now bust da b, 10x is now 6x + 4x
2x2+10x+12
2x2+6x+4x+12 Now factor this by grouping!!
(2x2+6x)+(4x+12)
2x(x+3)+4(x+3)
(2x+4)(x+3)
2(x+2)(x+3)

7. Factor 3x2 -7x -6 3x2 -7x -6 3x2 -9x + 2x -6 (3x2 -9x) + (2x -6)
a times c = -18, b = -7
So, what numbers when multiplied together give you -18 when added together give you -7?
-18 2 -9 -7
-9 and 2
3x2 -7x -6
3x2 -9x + 2x -6
(3x2 -9x) + (2x -6)
3x(x -3) + 2(x -3)

8. Factor 3x2 + 11x + 6 3x2 + 9x+2x + 6 (3x2 + 9x)+(2x + 6)18
Factor 3x2 + 11x + 6 9 2 11
3x2 + 9x+2x + 6
(3x2 + 9x)+(2x + 6)
3x(x+3) +2(x+3)
(3x +2)(x+3)
What 2 numbers when multiplied together give you 18,and when added give you 11?
9 and 2

9. Factor 4x2 - 14x + 6 24
-12 -2
-14
Since a times c is positive and b is negative both answers must be negative
4x2 - 14x + 6
4x2 - 12x -2x + 6
(4x2 - 12x) (-2x + 6)
4x(x - 3) -2(x - 3)
(4x - 2)(x - 3)
2(x - 2)(x - 3) +
2 is the gcf of (4x-2)
What 2 numbers when multiplied together give you 24,and when added give you -14?
-12 and -2

10. Factor - 8x2 - 47x + 6 - 8x2 - 47x + 6 - 8x2 - 48x+1x + 6
-48
Factor - 8x2 - 47x + 6
-48 1
-47
- 8x2 - 47x + 6
- 8x2 - 48x+1x + 6
- 8x(x+ 6)+1(x + 6)
(-8x+1)(x+6)
What 2 numbers when multiplied together give you -48,and when added give you -47?
-48 and 1

11. Factor 36x2 - 1 rewrite so 36x2 + 0x - 1 36x2 + 6x -6x - 1
-36 6 -6
rewrite so 36x2 + 0x - 1
36x2 + 6x -6x - 1
(36x2 + 6x)+(-6x - 1)
6x(6x + 1)+-1(6x +1)
(6x -1) (6x +1)
What 2 numbers when multiplied together give you -36,and when added give you 0?
-6 and 6