9-5: FACTORING TRINOMIALS OF THE TYPE X2 + BX + CEssential Question: How do you determine what numbers are used when factoring?

9-5: Factoring x2 + bx + c

No need to copy Factoring is FOIL-ing in reverse To factor a polynomial, you’ll need to

know how to find the possible factors of a number

List all of the factors of each number (on board) 24 12 54 15

9-5: Factoring x2 + bx + c

Factoring: The Steps Make sure the equation is written in standard

form f(x) = x2 + bx + c

Set up two parenthesis ( )( )

Find two numbers with A product of c A sum of b

Write answer as (x ± 1st number)(x ± 2nd number)

5-4: Factoring Quadratic Expressions

Multiply:+ number

Multiply:- number

Add:+ number

Add:- number

Add:+ number

Add:- number

Both #s are +

Both #s are -

Bigger # is +

Bigger # is -

Some hints about finding the two numbers to be used in factoring:

9-5: Factoring x2 + bx + c

Example #1: Factor x2 + bx + c Factor x2 + 7x + 12

Find the factors of 12. Which pair adds to 7? 1 & 12 2 & 6 3 & 4 Winner, winner

x2 + 7x + 12 = (x + 3)(x + 4)

9-5: Factoring x2 + bx + c

YOUR TURN Factor each expression g2 + 7g + 10

(g + 5)(g + 2) v2 + 21v + 20

(v + 20)(v + 1) a2 + 13a + 30

(a + 10)(a + 3)

9-5: Factoring x2 + bx + c

Example #2: Factor x2 – bx + c Factor d2 – 17d + 42

Find the factors of 42. Which pair adds to -17? -1 & -42 -2 & -21 -3 & -14 Works -6 & -7

d2 – 17d + 42 = (d – 3)(d – 14)

9-5: Factoring x2 + bx + c

YOUR TURN Factor each expression k2 – 10k + 25

(k – 5)(k – 5) x2 – 11x + 18

(x – 2)(x – 9) q2 – 15q + 36

(q – 12)(q – 3)

9-5: Factoring x2 + bx + c

Example #3: Factoring trinomials with a negative c Factor m2 + 6m – 27

Find the factors of 27. Which pair adds to 6? Because it adds to a +6, the bigger number is positive -1 & 27 -3 & 9 Got it

m2 + 6m – 27 = (m – 3)(m + 9) Factor p2 – 3p – 18

Find the factors of 18. Which pair adds to -3? Because it adds to a -3, the bigger number is negative 1 & -18 2 & -9 3 & -6 Got it

p2 – 3p – 18 = (p + 3)(p – 6)

9-5: Factoring x2 + bx + c

YOUR TURN Factor each expression m2 + 8m – 20

(m + 10)(m – 2) p2 – 3p – 40

(p – 8)(p + 5) y2 – y – 56

(y – 8)(y + 7)

9-5: Factoring x2 + bx + c

Assignment Worksheet #9-5 1 – 27, all