Warm-Up
Factor the trinomial
1. x2 – 10x +24
2. x2 + 10x +9
3. x2 + 6x – 40
4. x2 – 6x – 40
5. x2 – 11x + 24
Objective
The student will be able to:
factor quadratic trinomials of the
form ax2 + bx + c.
Review of Foil
c = pq
ax2 + bx + c = (mx + p)(nx + q)
a = mn
Example: 6x2 + 22x + 20 = (3x + 5)(2x + 4)
6=3*2
20 = 5 * 4
22 = (3 * 4) + (5 * 2)
1) Factor 3x2 + 5x + 2
Test the possible factors of a and c.
Try a = 3 * 1 and c = 1 * 2
(3x + 1)(1x + 2) = 3x2 + 7x + 2
Not correct!
Try a = 3 * 1 and c = 2 * 1
(3x + 2)(1x + 1) = 3x2 + 5x + 2
Correct!
2) Factor 2x2 + 21x – 11
Try all combinations of factors for a and c
Remember for c + - = + Factors of a and c
Product
Correct?
a = (1)(2) and c = (-1)(11)
(x – 1)(2x + 11) = 2x2 + 9x – 11
No
a = (1)(2) and c = (11)(-1)
(x + 11)(2x – 1) = 2x2 + 21x – 11
Yes
a = (1)(2) and c = (1)(-11)
(x + 1)(2x – 11) = 2x2 – 9x – 11
No
a = (1)(2) and c = (-11)(1)
(x – 11)(2x + 1) = 2x2 – 21x – 11
No
3) Factor 8x2 – 14x – 15
Try all combinations of factors for a and c
Remember for c - - = + Factors of a and c
Product
Correct?
a = (1)(8) and c = (-1)(15)
(x – 1)(8x + 15) = 8x2 + 7x – 15
No
a = (1)(8) and c = (15)(-1)
(x + 15)(8x – 1) = 8x2 + 119x – 15
No
a = (1)(8) and c = (3)(-5)
(x + 3)(8x – 5) = 8x2 + 19x – 15
No
a = (1)(8) and c = (-5)(3)
(x – 5)(8x + 3) = 8x2 – 37x – 15
No
a = (2)(4) and c = (-1)(15)
(2x – 1)(4x + 15) = 8x2 + 26x – 15
No
a = (2)(4) and c = (15)(-1)
(2x + 15)(4x – 1) = 8x2 + 58x – 15
No
a = (2)(4) and c = (3)(-5)
(2x + 3)(4x – 5) = 8x2 + 2x – 15
No
a = (2)(4) and c = (-5)(3)
(2x – 5)(4x + 3) = 8x2 – 14x – 15
Yes
4) Factor 6x2 – 2x – 8
Is there a common factor?
Factor 2 out of the expression first
6x2 – 2x – 8 = 2(3x2 – x – 4)
Now factor the remaining expression
Factors of a and c
Product
Correct?
a = (1)(3) and c = (-1)(4)
(x – 1)(3x + 4) = 3x2 + x – 4
No
a = (1)(3) and c = (4)(-1)
(x + 4)(3x – 1) = 3x2 + 11x – 4
No
a = (1)(3) and c = (1)(-4)
(x + 1)(3x – 4) = 3x2 – x – 4
Yes
a = (1)(3) and c = (-4)(1)
(x – 4)(3x + 1) = 3x2 – 11x – 4
No
a = (1)(3) and c = (-2)(2)
(x – 2)(3x + 2) = 3x2 – 4x – 4
No
a = (1)(3) and c = (2)(-2)
(x + 2)(3x – 2) = 3x2 + 4x – 4
No
Homework
p614 #15 – 32