1. 8.8: FACTORING BY GROUPING: Higher Degree Polynomials: Polynomials with a degree higher than 2.

2. FACTORING ax 2 + bx + c Procedure: 1) Always look for the GCF of all the terms 2) Factor the remaining terms – pay close attention to the value of coefficient a and follow the proper steps. 3) Re-write the original polynomial as a product of the polynomials that cannot be factored any further.

3. GOAL:

4. FACTORING: By Grouping Ex: What is the FACTORED form of: 3n 3 -12n 2 +2n-8?

5. SOLUTION: To factor a polynomial by grouping we group terms that have a GCF: Look at GCF of each: 3n 3 -12n 2 Now take the GCF of the two: Factored form : (n-4)(3n 2 +2) 3n 3 -12n 2 +2n-8  3n 3 -12n 2 +2n-8  3n 2 (n-4) 2n-8  2(n-4) 3n 2 (n-4) +2 (n-4)

6. YOU TRY IT: Ex: What is the FACTORED form of: 8t 3 +20t+14t 2 +35?

7. SOLUTION: To factor a polynomial by grouping we group terms that have a GCF: Look at GCF of each: 8t 3 +14t 2 Now take the GCF of the two: Factored form : (4t+7)(2t 2 +5) 8t 3 +14t 2 +20t+35  8t 3 +14t 2 +20t+35  2t 2 (4t+7) 20t+35  5(4t+7) 2t 2 (4t+7) +5(4t+7)

8. YOU TRY IT: Ex: What is the FACTORED form of: 4q 4 -8q 3 +12q 2 -24q?

9. SOLUTION: Before we group, we must again go back to the first step of factoring: 1) Factor what is in common? 4q 4 -8q 3 +12q 2 -24q? 4q(q 3 -2q 2 +3q-6)

10. SOLUTION: To factor a polynomial by grouping we group terms that have a GCF: Look at GCF of each: q 3 -2q 2 Now take the GCF of the two: Factored form : 4q (q-2) (q 2 +3) 4q(q 3 -2q 2 +3q-6)  4q(q 3 -2q 2 +3q-6)  q 2 (q-2) 3q-6  3(q-2) q 2 (q-2) +3(q-2)

11. REAL-WORLD: The area of a square rug is given by 4x 2 -100. What are the possible dimensions of the rug?

12. SOLUTION: To factor a difference of two squares with a coefficient ≠ 1 we still follow the factoring procedure: 4x 2 -100 ax 2 +c  a= +1  c =-25 Look at the factors of a and c:  a : (1)(1)c: (-5)(5) We now see that the factored form is: 4(x-5)(x+5)  4(x 2 -25)

13. NOW SOLVE THIS:

14. VIDEOS: Factoring Quadratics Factoring by Grouping: http://www.khanacademy.org/math/algebra/quadratics/f actoring_quadratics/v/factoring-trinomials-with-a-non-1- leading-coefficient-by-grouping http://www.khanacademy.org/math/algebra/quadratics/ factoring_quadratics/v/ex2-factoring-quad

15. VIDEOS: Factoring Quadratics Factoring by Grouping: http://www.khanacademy.org/math/algebra/quadratics/f actoring_quadratics/v/factoring-trinomials-by-grouping-5 http://www.khanacademy.org/math/algebra/quadratics/fa ctoring_quadratics/v/factoring-trinomials-by-grouping-6

16. CLASSWORK: Page 514-516: Problems: 1, 2, 3, 9, 13, 16, 22, 27, 30, 32, 37, 45.