1. 8-2 Factoring by GCF Multiplying and Factoring

2. 8-2 Factoring by GCF Multiplying and Factoring Lesson 9-2 Simplify –2g 2 (3g 3 + 6g – 5). –2g 2 (3g 3 + 6g – 5) = –2g 2 (3g 3 ) –2g 2 (6g) –2g 2 (–5)Use the Distributive Property. = –6g 2 + 3 – 12g 2 + 1 + 10g 2 Multiply the coefficients and add the exponents of powers with the same base. = –6g 5 – 12g 3 + 10g 2 Simplify.

3. 8-2 Factoring by GCF 4) Simplify: 4t 2 (3t 2 + 2t - 5) 12t 4 5) Simplify: - 4m 3 (-3m - 6n + 4p) 12m 4 + 8t 3 - 20t 2 + 24m 3 n- 16m 3 p

4. 8-2 Factoring by GCF Additional Example 1A: Factoring by Using the GCF Factor each polynomial. Check your answer. 2x 2 – 4 2x 2 = 2  x  x 4 = 2  2 2 Find the GCF. The GCF of 2x 2 and 4 is 2. Write terms as products using the GCF as a factor. 2x 2 – (2  2) 2(x 2 – 2) Check 2(x 2 – 2) 2x 2 – 4 Multiply to check your answer. The product is the original polynomial. Use the Distributive Property to factor out the GCF.

5. 8-2 Factoring by GCF Additional Example 1B: Factoring by Using the GCF Factor each polynomial. Check your answer. 8x 3 – 4x 2 – 16x 2x 2 (4x) – x(4x) – 4(4x) 4x(2x 2 – x – 4) 8x 3 – 4x 2 – 16x 8x 3 = 2  2  2  x  x  x 4x 2 = 2  2  x  x 16x = 2  2  2  2  x 2  2  x = 4x Find the GCF. The GCF of 8x 3, 4x 2, and 16x is 4x. Write terms as products using the GCF as a factor. Use the Distributive Property to factor out the GCF. Multiply to check your answer. The product is the original polynomial. Check

6. 8-2 Factoring by GCF Additional Example 1C: Factoring by Using the GCF Factor each polynomial. Check your answer. – 14x – 12x 2 – 1(14x + 12x 2 ) Both coefficients are negative. Factor out –1. Find the GCF. The GCF of 14x and 12x 2 is 2x. – 1[7(2x) + 6x(2x)] – 1[2x(7 + 6x)] – 2x(7 + 6x) Write each term as a product using the GCF. Use the Distributive Property to factor out the GCF. 14x = 2  7  x 12x 2 = 2  2  3  x  x 2  x = 2x

7. 8-2 Factoring by GCF Additional Example 1C Continued Factor each polynomial. Check your answer. – 14x – 12x 2 Check – 2x(7 + 6x) Multiply to check your answer. The product is the original polynomial. – 14x – 12x 2

8. 8-2 Factoring by GCF When you factor out –1 as the first step, be sure to include it in all the other steps as well. Caution!

9. 8-2 Factoring by GCF Additional Example 1D: Factoring by Using the GCF Factor each polynomial. Check your answer. 3x 3 + 2x 2 – 10 10 = 2  5 Find the GCF. There are no common factors other than 1. The polynomial cannot be factored further. 3x 3 + 2x 2 – 10 3x 3 = 3  x  x  x 2x 2 = 2  x  x

10. 8-2 Factoring by GCF Check It Out! Example 1a Factor each polynomial. Check your answer. 5b + 9b 3 5b = 5  b 9b = 3  3  b  b  b b 5(b) + 9b 2 (b) b(5 + 9b 2 ) Check 5b + 9b 3 Find the GCF. The GCF of 5b and 9b 3 is b. Multiply to check your answer. The product is the original polynomial. Write terms as products using the GCF as a factor. Use the Distributive Property to factor out the GCF.

11. 8-2 Factoring by GCF Check It Out! Example 1b Factor each polynomial. Check your answer. 9d 2 – 8 2 Find the GCF. There are no common factors other than 1. The polynomial cannot be factored further. 9d 2 – 8 2 9d 2 = 3  3  d  d 8 2 = 2  2  2  2  2  2

12. 8-2 Factoring by GCF Check It Out! Example 1c Factor each polynomial. Check your answer. – 18y 3 – 7y 2 – 1(18y 3 + 7y 2 ) Both coefficients are negative. Factor out –1. Find the GCF. The GCF of 18y 3 and 7y 2 is y 2. 18y 3 = 2  3  3  y  y  y 7y 2 = 7  y  y y  y = y 2 Write each term as a product using the GCF. Use the Distributive Property to factor out the GCF. – 1[18y(y 2 ) + 7(y 2 )] – 1[y 2 (18y + 7)] – y 2 (18y + 7)

13. 8-2 Factoring by GCF Check It Out! Example 1c Continued Factor each polynomial. Check your answer. – 18y 3 – 7y 2 Check – y 2 (18y + 7) Multiply to check your answer. The product is the original polynomial. – 18y 3 – 7y 2

14. 8-2 Factoring by GCF Check It Out! Example 1d Factor each polynomial. Check your answer. 8x 4 + 4x 3 – 2x 2 8x 4 = 2  2  2  x  x  x  x 4x 3 = 2  2  x  x  x 2x 2 = 2  x  x 2  x  x = 2x 2 4x 2 (2x 2 ) + 2x(2x 2 ) – 1(2x 2 ) 2x 2 (4x 2 + 2x – 1) Check 2x 2 (4x 2 + 2x – 1) 8x 4 + 4x 3 – 2x 2 The GCF of 8x 4, 4x 3 and 2x 2 is 2x 2. Multiply to check your answer. The product is the original polynomial. Write terms as products using the GCF as a factor. Use the Distributive Property to factor out the GCF. Find the GCF.