2. Lesson 10.5: Factoring x2 + bx + c
Recall: Using Foil
(x + 3)(x + 7) = ?
x2 + 10x + 21
How can we go backward?
Factor x2 + 10x + 21
(x + 3)(x + 7)

3. “Grind it out “ method of factoring
Factoring x2 + bx + c
**** Looking for factors of “c” whose sum is “b”
- Factors are two binomials
- the first term of each binomial = square root
of first term of trinomial
- second terms of binomials = factors of “c”,
whose sum is “b”

4. Factor completely.
x2 + 8x + 15
2) x2 + 11x + 10
( )( )
(x + 10)(x + 1)
x x
x2 – 17x + 60
(x – 12) ( x – 5)
x2 – 9x + 20
(x – 4)(x – 5)

5. Factor completely.
x2 – 8x – 9
(x – 9)( x + 1)
x2 + 2x – 48
(x + 8)(x – 6)

6. When factoring x2 + bx + c
IF b and c are positive, use positive factors of c
IF b is negative and c is positive, use negative factors of c.
IF c is negative, use one positive factor of c and one negative factor of c.

7. Factoring Steps:
1) Look for GCMF
2) Look for Diff. Of two squares
3) Look for Trinomial Square
4) Grind it out

8. x2 – 5x = 24
x2 – 5x – 24 = 24 – 24
x2 – 5 x – 24 = 0
(x – 8)(x + 3) = 0
x – 8 = or x + 3 = 0
x – = 0 + 8
x = 8
x + 3 – 3 = 0 – 3
x = - 3
x = {-3, 8}

9. Discriminant of a quadratic expression:
b2 – 4ac
Quadratic Expression is factorable if the discriminant is a perfect square
Expression is PRIME if the discriminant is NOT a perfect square
Ex. Determine if factorable or prime
x2 + 6x – ) x2 + 6x – 8
62 – 4(1)(7)
36 – 28
8 PRIME
62 – 4(1)(8)
36 -32
4 Factorable

10. Homework : p.607, #12-46 evens

11. Factor:
x2 – 14x + 24
(x – 12)(x – 2)
x2 + 20x + 36
(x + 18)(x + 2)

12. Solve.
x2 + 11x + 18 = 0
(x + 9)(x + 2) = 0
x + 9 = or x + 2 = 0
x + 9 – 9 = 0 – 9
x = -9
x + 2 – 2 = 0 – 2
x = -2
x = {-2, -9}