8.8: FACTORING BY GROUPING:

Higher Degree Polynomials: Polynomials with a degree higher than 2.

FACTORING ax2 + bx + c Procedure:

1) Always look for the GCF of all the terms2) 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:

3n3-12n2+2n-8?

SOLUTION: To factor a polynomial by grouping we group terms that have a GCF:

Look at GCF of each: 3n3-12n2

Now take the GCF of the two:

Factored form : (n-4)(3n2+2)

3n3-12n2+2n-8 3n3-12n2+2n-8

3n2(n-4) 2n-8 2(n-4)

3n2 (n-4) +2 (n-4)

YOU TRY IT:

Ex: What is the FACTORED form of:

8t3+20t+14t2+35?

SOLUTION: To factor a polynomial by grouping we group terms that have a GCF:

Look at GCF of each: 8t3+14t2

Now take the GCF of the two:

Factored form : (4t+7)(2t2+5)

8t3+14t2+20t+35 8t3+14t2+20t+35

2t2(4t+7) 20t+35 5(4t+7)

2t2 (4t+7) +5(4t+7)

YOU TRY IT:

Ex: What is the FACTORED form of:

4q4-8q3+12q2-24q?

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)

SOLUTION: To factor a polynomial by grouping we group terms that have a GCF:

Look at GCF of each: q3-2q2

Now take the GCF of the two:

Factored form : 4q (q-2) (q2+3)

4q(q3-2q2+3q-6) 4q(q3-2q2+3q-6)

q2(q-2) 3q-6 3(q-2)

q2 (q-2) +3(q-2)

REAL-WORLD:

The area of a square rug is given by 4x2-100.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:

4x2-100ax2+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(x2-25)

NOW SOLVE THIS:

VIDEOS: FactoringQuadratics

Factoring by Grouping:

Factoring by Grouping:http://www.khanacademy.org/math/algebra/quadratics/factoring_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

VIDEOS: FactoringQuadratics

Factoring by Grouping:

Factoring by Grouping:

http://www.khanacademy.org/math/algebra/quadratics/factoring_quadratics/v/factoring-trinomials-by-grouping-5

http://www.khanacademy.org/math/algebra/quadratics/factoring_quadratics/v/factoring-trinomials-by-grouping-6

CLASSWORK:

Page 514-516:

Problems: 1, 2, 3, 9, 13, 16, 22, 27, 30, 32, 37, 45.