Lesson #7 Trinomial Factoring

Recall that we have learnt how to factor a polynomial 3 ways so far.

(3b - 2)=(a + 1)

2x3y2 + 4x2y5 – 16x4y3

=2x2y2 (x + 2y3 – 8x2y)Common Factoring

6ab + 3b – 4a - 2

=3b(2a + 1) - 2(2a + 1) Group Factoring

(25x2 – 16y2)

= (5x – 4y) (5x + 4y)Difference of SquaresFactoring

There is another way. If it is a trinomial of the form

where b and c are integers, we use what we call Munchkin Numbers.

Expand using FOIL

=x2 +mx +nx + mn=x2 +(m+n)x + mn

x2 +bx + c

(x + n)(x + m)

b equals the sum of 2 numbers:

c equals the product of 2 numbers

b = m+n

c = mn

=(x + )(x + )

eg. 1 Factor these trinomials

4 2

2. x2 + 7x + 12

4=(x + )(x + )3

3. x2 -2x - 15

5=(x - )(x + )3

4. x2 + 7x - 30

3=(x - )(x + )10

5. x2 - 13x + 42

7=(x - )(x - )6

6. a2 -5 ab + 4b2

4b=(a - )(a - )b

1. x2 + 6x + 8

There is another case for trinomials of the form

Again, a, b and c are integers.

For these problems, use group factoring.

=ax2 +mx +nx + c

ax2 +bx + c

ax2 + bx + c

eg. 2 2x2 + 8x + 6

=2x2 + 6x +2x + 6

=2x(x + 3) +2(x + 3)

=(x + 3)(2x+2)

=(6x + )(x - ) =(3x - )(2x - )

=(3x + )(x - ) =(2x + )(x + )

eg. 3 Or use a try and error method

1. 2x2 - 5x + 2

1 4

2. 3x2 - 5x - 12

4 3

3. 6x2 -11x + 4

4 1

4. 6x2 -29x - 5

1 5

Homework

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