Factoring Trinomials

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12 = 1 • 12

= 2 • 6

= 3 • 4

Step 3: Which pair adds up to 11?

Step 1: Multiply 3 • 4 = 12 (the leading coefficient & constant).

None of the pairs add up to 11, this trinomial can’t be factored; it is PRIME.

Slide 16

Factor each trinomial, if possible. The first four do NOT have leading coefficients, the last two DO have leading coefficients. Watch out for signs!!

1) t2 – 4t – 21

2) x2 + 12x + 32

3) x2 –10x + 24

4) x2 + 3x – 18

5) 2x2 + x – 21

6) 3x2 + 11x + 10

Factor These Trinomials!

Slide 17

Solution #1:

t2 – 4t – 21

1) Factors of -21:

1 • -21, -1 • 21

3 • -7, -3 • 7

2) Which pair adds to (- 4)?

3) Write the factors.

t2 – 4t – 21 = (t + 3)(t - 7)

Slide 18

Solution #2:

x2 + 12x + 32

1) Factors of 32:

1 • 32

2 • 16

4 • 8

2) Which pair adds to 12 ?

3) Write the factors.

x2 + 12x + 32 = (x + 4)(x + 8)

Slide 19

Solution #3:

x2 - 10x + 24

1) Factors of 32:

1 • 24

2 • 12

3 • 8

4 • 6

2) Which pair adds to -10 ?

3) Write the factors.

x2 - 10x + 24 = (x - 4)(x - 6)

None of them adds to (-10). For the numbers to multiply to +24 and add to -10, they must both be negative!

-1 • -24

-2 • -12

-3 • -8

-4 • -6

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Solution #4:

x2 + 3x - 18

1) Factors of -18:

1 • -18, -1 • 18

2 • -9, -2 • 9

3 • -6, -3 • 6

2) Which pair adds to 3 ?

3) Write the factors.

x2 + 3x - 18 = (x - 3)(x + 18)

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Solution #5:

2x2 + x - 21

1) Multiply 2 • (-21) = - 42; list factors of - 42.

1 • -42, -1 • 42

2 • -21, -2 • 21

3 • -14, -3 • 14

6 • -7, -6 • 7

2) Which pair adds to 1 ?

3) Write the temporary factors.

2x2 + x - 21 = (x - 3)(2x + 7)

( x - 6)( x + 7)

4) Put “2” underneath.

5) Reduce (if possible).

3

6) Move denominator(s)in front of “x”.

( x - 3)( 2x + 7)

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Solution #6:

3x2 + 11x + 10

1) Multiply 3 • 10 = 30; list factors of 30.

1 • 30

2 • 15

3 • 10

5 • 6

2) Which pair adds to 11 ?

3) Write the temporary factors.

3x2 + 11x + 10 = (3x + 5)(x + 2)

( x + 5)( x + 6)

4) Put “3” underneath.

5) Reduce (if possible).

2

6) Move denominator(s)in front of “x”.

( 3x + 5)( x + 2)