8 8 FACTORING BY GROUPING Higher Degree Polynomials

8. 8: FACTORING BY GROUPING: Higher Degree Polynomials: Polynomials with a degree higher than 2.

FACTORING 2 ax + 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.

GOAL:

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

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

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

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

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

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

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

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

SOLUTION: To factor a difference of two squares with a coefficient ≠ 1 we still follow the factoring procedure: 2 ax +c 4 x 2 -100 4(x 2 -25) 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)

NOW SOLVE THIS:

VIDEOS: Factoring Quadratics 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/ex 2 -factoring-quad

VIDEOS: Factoring Quadratics 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/f actoring_quadratics/v/factoring-trinomials-by-grouping-6

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