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8.8: FACTORING BY GROUPING:

Higher Degree Polynomials : Polynomials with a degree higher than 2 . 8.8: FACTORING BY GROUPING:. Procedure:. 1) Always look for the GCF of all the terms. FACTORING ax 2 + bx + c .

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8.8: FACTORING BY GROUPING:

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

  2. Procedure: 1) Always look for the GCF of all the terms FACTORING ax2 + bx + c 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: 3n3-12n2+2n-8?

  5. SOLUTION: To factor a polynomial by grouping we group terms that have a GCF: 3n3-12n2+2n-8 3n3-12n2+2n-8 Look at GCF of each: 3n3-12n2  3n2(n-4) 2n-8  2(n-4) Now take the GCF of the two: 3n2 (n-4) +2 (n-4) Factored form : (n-4)(3n2+2)

  6. YOU TRY IT: Ex: What is the FACTORED form of: 8t3+20t+14t2+35?

  7. SOLUTION: To factor a polynomial by grouping we group terms that have a GCF: 8t3+14t2+20t+35 8t3+14t2+20t+35 Look at GCF of each: 8t3+14t2  2t2(4t+7) 20t+35  5(4t+7) Now take the GCF of the two: 2t2 (4t+7) +5(4t+7) Factored form : (4t+7)(2t2+5)

  8. YOU TRY IT: Ex: What is the FACTORED form of: 4q4-8q3+12q2-24q?

  9. SOLUTION: Before we group, we must again go back to the first step of factoring:1) Factor what is in common? 4q4-8q3+12q2-24q? 4q(q3-2q2+3q-6)

  10. SOLUTION: To factor a polynomial by grouping we group terms that have a GCF: 4q(q3-2q2+3q-6)  4q(q3-2q2+3q-6) Look at GCF of each: q3-2q2  q2(q-2) 3q-6  3(q-2) Now take the GCF of the two: q2 (q-2) +3(q-2) Factored form : 4q (q-2) (q2+3)

  11. REAL-WORLD: The area of a square rug is given by 4x2-100.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: 4x2-100  4(x2-25) ax2+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)

  13. NOW SOLVE THIS:

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

  15. VIDEOS: FactoringQuadratics Factoring by Grouping: http://www.khanacademy.org/math/algebra/quadratics/factoring_quadratics/v/factoring-trinomials-by-grouping-5 Factoring by Grouping: http://www.khanacademy.org/math/algebra/quadratics/factoring_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.

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