Alg1 Notes 7.5.notebook
March 07, 2013
7­5 Factoring Special Products
Skills we've learned
Factor each polynomial. 1. 5x2 + 17x + 6 2. 2x2 + 5x – 12 3. 6x2 – 23x + 7 5. –2x2 + 7x – 3 4. –4x2 + 11x + 20
6. 8x2 + 27x + 9
Skills we need
Determine whether the following are perfect squares. If so, find the square root. 1) 64
2) 36
3) 45
2
8
4) x
5) y 6) 4x6 7) 9y7
8) 49p10 Warm­up Answers
Alg1 Notes 7.5.notebook
March 07, 2013
7­5 Factoring Special Products
1. Factor perfect­square trinomials
2. Factor the difference of two squares
Land Planning
I. Recognizing Perfect­Square Trinomials
A trinomial is a perfect square if: • The first and last terms are perfect squares.
• The middle term is two times one factor from the first term and one factor from the last term.
Alg1 Notes 7.5.notebook
March 07, 2013
Circle each trinomial that is a perfect square. 2. 81x2 + 90x + 25
1. 9x2 – 15x + 64
4. x2 + 4x + 4
3. 6x2 – 10x + 14
5. 9x2 – 6x + 4
II. Factoring Perfect Square Trinomials
Factor each trinomial that is a perfect square. 2. 81x2 + 90x + 25
4. x2 + 4x + 4
Alg1 Notes 7.5.notebook
March 07, 2013
Factor each trinomial that is a perfect square. 6. 4x2 + 12x + 9
7. 100x2 + 140x + 49
III. Recognizing the Difference of Two Squares
9. 3p2 – 9q4 10. 100x2 – 4y2 Alg1 Notes 7.5.notebook
March 07, 2013
Circle each binomial that is a difference of two squares. 11. x4 – 25y6 13. p8 + 49q6 12. 1 – 4x2 14. 16x2 – 4y5 IV. Factoring the Difference of Two Squares
Factor each binomial that is a difference of two squares. 15. x2 – 16 16. 100x4 – y6 Alg1 Notes 7.5.notebook
March 07, 2013
Factor each binomial that is a difference of two squares. 17. 25x2 – 49 18. 64x4 – y6 V. Application
19. A square piece of cloth must be cut to make a tablecloth. The area needed is (16x2 – 24x + 9) in2. The dimensions of the cloth are of the form cx – d, where c and d are whole numbers. Find an expression for the perimeter of the cloth. Find the perimeter when x = 11 inches.
When x = 11 in. the perimeter of the tablecloth is 164 in.
Alg1 Notes 7.5.notebook
March 07, 2013
7.5 p.494 #3, 6, 7, 9, 12, 18, 20, 24, 27 ­ 31, 38, 41, 46