8-9 - Study Guide and Intervention PDF

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8-9 - Study Guide and Intervention

Study Guide and Intervention 16n2 - 24n + 9 is a perfect square trinomial. ... 6. 81 + 18j + j2. 2(7x + 10y)(7x - 10y). (x + 11)2. (9 + j)2.

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NAME DATE PERIOD NAME DATE PERIOD Lesson 8-9

Chapter 8 57 Glencoe Algebra 1

Factor Perfect Square Trinomials

The patterns shown below can be used to factor perfect square trinomials .Study Guide and Intervention

Perfect Squares

Determine whether

16 n 2 - 24n + 9 is a perfect square trinomial. If so, factor it.

Since 16

n 2 = (4n)(4n), the first term is a perfect square.

Since 9

3 ? 3, the last term is a perfect square.

The middle term is equal to 2(4

n )(3).

Therefore, 16

n 2 - 24n + 9 is a perfect square trinomial. 16 n 2 - 24n + 9 = (4n) 2 - 2(4n)(3) + 3 2 = (4n - 3) 2

Factor 16x

2 - 32x + 15.

Since 15 is not a perfect square, use a different

factoring pattern. 16 x 2 - 32x + 15 Original trinomial = 16x 2 + mx + px + 15 Write the pattern. = 16x 2 - 12x - 20x + 15 m = -12 and p = -20 = (16x 2 - 12x) - (20x - 15) Group terms. = 4x(4x - 3) - 5(4x - 3) Find the GCF. = (4x - 5)(4x - 3) Factor by grouping.

Therefore 16

x 2 - 32x + 15 = (4x - 5)(4x - 3).

Exercises

Determine whether each trinomial is a perfect square trinomial. Write yes or no.

If so, factor it.

1. x 2 - 16x + 64 2. m 2 + 10m + 25 3. p

2 + 8p + 64

yes; ( x - 8)(x - 8) yes; (m + 5)(m + 5) no Factor each polynomial, if possible. If the polynomial cannot be factored, write prime

4. 98x

2 - 200y 2 5. x 2 + 22x + 121 6. 81 + 18j + j 2 2(7 x + 10y)(7x - 10y) (x + 11) 2 (9 + j) 2

7. 25c

2 - 10c - 1 8. 169 - 26r + r 2 9. 7x 2 - 9x + 2 prime (13 - r)2 (7x - 2)(x - 1)

10. 16m

2 + 48m + 36 11. 16 - 25a 2 12. b 2 - 16b + 256 4(2 m + 3) 2 (4 + 5a)(4 - 5a) prime

13. 36x

2 - 12x + 1 14. 16a 2 - 40ab + 25b 2

15. 8m

3 - 64m (6 x - 1) 2 (4a - 5b) 2 8m(m 2 - 8)Example 1Example 2

Perfect Square Trinomiala trinomial of the form a

2 + 2ab + b 2 or a 2 - 2ab + b 2 Squaring a Binomial Factoring a Perfect Square Trinomial a + 4)2 = a 2 + 2(a)(4) + 4 2 a 2 + 8a + 16a 2 + 8a + 16 = a 2 + 2(a)(4) + 4 2 (a + 4) 2 (2 x - 3) 2 (2 x 2 -2(2x)(3) + 3 2 4x 2 - 12x + 94x 2 - 12x + 9 = (2x) 2quotesdbs_dbs7.pdfusesText_5

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