Multiply (x+3)(2x-7) Factor 3. 42x – 7 Warm-Up Multiply (x+3)(2x-7) Factor 3. 42x – 7

Homework Check

Factoring Trinomials and Difference of Two Perfect Squares

Sign Rule for Factoring Trinomials: When the last term is POSITIVE… The signs inside the parenthesis will be the SAME as the middle number’s sign

x2 +7x + 6 ( )( ) x x + 6 + 1

x2 + 9x + 14 ( )( ) x x + 7 + 2

x2 – 6x + 8 ( )( ) x x – 4 – 2

x2 – 10x + 16 ( )( ) x x – 8 – 2

Sometimes you can factor out a GCF 1st!

2x2 – 16x + 24 2(x2 – 8x +12) 2( )( ) x x – 6 – 2

You Try... 3y2 + 36y + 60 3(y +10)(y +2) 4x2 +24x + 32 4(x + 2)(x + 4)

Sign Rule for Factoring Trinomials: When the last term is NEGATIVE… The parenthesis will have DIFFERENT SIGNS. The larger factor will have the SAME sign as the middle number

n2 + 2n – 48 ( )( ) n n + 8 – 6

x2 + 8x – 20 ( )( ) x x – 2 + 10

x2 – 4x – 21 ( )( ) x x + 3 – 7

x2 – 9x – 36 ( )( ) x x + 3 – 12

2x3 + 18x2 + 28x

c4 + 2c3 – 80c2

3x2 + 6x – 24

5x2 + 5x – 10

3x3 – 6x2 – 45x

3x3 – 39x2 + 120x

Difference of Two Perfect Squares

Factoring Difference of Two Squares Both terms must be Perfect Squares and have a MINUS between them Check the binomial for GCF Use two sets of parenthesis (one’s a plus, one’s a minus) Split up what it takes to make the 1st a perfect square and what it takes the 2nd to be a perfect square

Difference of Two Squares Factor

Difference of Two Squares Factor

2x3 – 162x

16x2 – 36

Factoring Trinomials when a is not equal to 1 Guess & Check Method

How to Factor a Trinomial Check for GCF 1st. Divide out the GCF of each term if one exists. When factoring ax2 + bx + c, first find factors of a and c. Check the products of the inner and outer terms to see if the sum is b. When c is POSITIVE, both signs inside the parentheses will be the same as the middle term.

1. x2 + 9x + 14 +1 +2 +14 +7 1x ( + )( + ) x x 2 7

2. 2x2 – 5x + 3 1x 2x -1 -3 ( – )( – ) x 2x 1 3

3. 5x2 + 11x + 2 1x 5x +1 +2 ( + )( + ) x 5x 2 1

4. 3x2 – 10x + 3 1x 3x -1 -3 ( – )( – ) x 3x 3 1

5. 2x2 – 7x + 5 1x 2x -1 -5 ( – )( – ) x 2x 1 5

6. 6x2 – 11x + 3 1x 2x 6x 3x -1 -3 ( – )( – ) 2x 3x 3 1

7. 4x2 + 16x + 15 +1 +15 +3 +5 1x 2x 4x ( + )( + ) 2x 2x 3 5

8. 3x2 – 20x – 7 1x 3x 1 7 ( )( ) x 3x – + 7 1

9. 2x2 + 3x – 5 1x 2x 1 5 ( )( ) x 2x – + 1 5

10. 5m2 + 14m – 3 1m 5m 1 3 ( )( ) m 5m + – 3 1

11. 2x2 – 11x – 21 1x 2x 1 3 7 21 ( )( ) x 2x – + 7 3

Sometimes you can factor out a GCF 1st!

12. 14x2 – 32x + 18 2(7x2 – 16x + 9) 2( – )( – ) x 7x 1 9 1x 7x -1 -9 -3 2( – )( – ) x 7x 1 9

Work Factoring WS