Factoring Trinomials and Difference of Two Perfect Squares

Explore the concept of factoring trinomials and difference of two perfect squares through step-by-step examples and visual aids. Understand the sign rules for factoring trinomials with positive and negative last terms. Learn how to factor out a greatest common factor and practice factoring various quadratic expressions effectively.

• Factoring
• Trinomials
• Perfect Squares
• Sign Rules
• Quadratic Expressions

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1. Opener Multiply 1. (x+3)(2x-7) 3 2 2. 6 (5 x x 4 x 7) Factor 3. 42x 7 5 6 9 4. 36 x 18 x 45 x +

2. Homework Check

3. Skills Check

4. Factoring Trinomials and Difference of Two Perfect Squares

5. Sign Rule for Factoring Trinomials: When the last term is POSITIVE The signs inside the parenthesis will be the SAME Look at b for the sign Front are factors of a Last factors of c that will add to get b.

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

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

8. x2 6x + 8 ( )( ) x 4 x 2

9. Sometimes you can factor out a GCF 1st!

10. x2 10x + 16 ( )( ) x 8 x 2

11. 2x2 16x + 24 2(x2 8x +12) 2( )( ) x 6 x 2

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

13. 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

14. n2 + 2n 48 ( )( ) n + 8 n 6

15. x2 + 8x 20 ( )( ) x + 10 x 2

16. x2 4x 21 ( )( ) x + 3 x 7

17. x2 9x 36 ( )( ) x + 3 x 12

18. c4 + 2c3 80c2 ( ) 8 + 2 2 2 80 c c c )( ( ) + 2 10 c c c

19. 3x2 + 6x 24 ( ) + 2 3 2 8 x x ( )( ) + 3 4 2 x x

20. Opener Match the problems with the signs of the factors. A.x2 - 6x + 8 i. Both signs are positive. B.x2 + 6x + 8 ii. Both signs are negative. C. x2 - 7x - 8 iii. They have different signs.

21. 2x3 + 18x2 + 28x ( ) + + 2 2 9 14 x x x ( )( ) + + 2 7 2 x x x

22. 5x2 + 5x 10 ( ) + )( 2 2 5 ( 2 x x ) + 5 1 x x

23. 3x3 6x2 45x ( ( ) 2 3 2 )( 15 ) 3 x x x + 3 5 x x x

24. 3x3 39x2 + 120x ( ( ) ) + 2 3 13 )( 5 40 x x x 3 8 x x x

25. Difference of Two Perfect Squares

26. Factoring Difference of Two Squares 1. Both terms must be Perfect Squares and have a MINUS between them 2. Check the binomial for GCF 3. Use two sets of parenthesis (one s a plus, one s a minus) 4. Split up what it takes to make the 1st a perfect square and what it takes the 2nd to be a perfect square

27. Difference of Two Squares Factor 2 1. 25 n ( n = )( ) + 5 5 n 2 ( 2 2. 4 121 x + x y )( ) = 2 11 2 11 y x y

28. Difference of Two Squares Factor 2 3. 196r 1 ( 14 = )( ) + 1 14 1 r r x ( 10 2 4. 100 49 + )( ) = 7 10 7 x x

29. 2x3 162x ( ) x x 2 2 81 ( )( ) + 2 9 9 x x x

30. 16x2 36 ( ) x 2 4 4 9 ( )( ) + 4 2 3 2 3 x x

31. Classwork Worksheet