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
3n -12n +2n-8?
SOLUTION: To factor a polynomial by grouping
we group terms that have a GCF:
3
2
3
2
3n -12n +2n-8 3n -12n +2n-8
Look at GCF of each:
3
2
3n -12n
2n-8

2
3n (n-4)
 2(n-4)
Now take the GCF of the two:
2
3n (n-4)
Factored form :
+2 (n-4)
2
(n-4)(3n +2)
YOU TRY IT:
Ex:
What is the FACTORED form of:
3
2
8t +20t+14t +35?
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:
3
2
8t +14t

2
2t (4t+7)
20t+35  5(4t+7)
Now take the GCF of the two:
2
2t (4t+7)
Factored form :
+5(4t+7)
2
(4t+7)(2t +5)
YOU TRY IT:
Ex:
What is the FACTORED form of:
4
3
2
4q -8q +12q -24q?
SOLUTION:
Before we group, we must again go back to the
first step of factoring:
1) Factor what is in common?
4
3
2
4q -8q +12q -24q?
3
2
4q(q -2q +3q-6)
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:
3
2
q -2q
3q-6

2
q (q-2)
 3(q-2)
Now take the GCF of the two:
2
q (q-2)
+3(q-2)
Factored form : 4q (q-2)
2
(q +3)
REAL-WORLD:
The area of a
square rug is given
by
2
4x -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
4x2-100  4(x2-25)
 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/f
actoring_quadratics/v/factoring-trinomials-with-a-non-1leading-coefficient-by-grouping
Factoring by Grouping:
http://www.khanacademy.org/math/algebra/quadratics/
factoring_quadratics/v/ex2-factoring-quad
VIDEOS:
Factoring
Quadratics
Factoring by Grouping:
http://www.khanacademy.org/math/algebra/quadratics/f
actoring_quadratics/v/factoring-trinomials-by-grouping-5
Factoring by Grouping:
http://www.khanacademy.org/math/algebra/quadratics/fa
ctoring_quadratics/v/factoring-trinomials-by-grouping-6
CLASSWORK:
Page 514-516:
Problems: 1, 2, 3, 9, 13,
16, 22, 27, 30,
32, 37, 45.