Section 6.1
1;
Factoring Polynomials with Common
Factors
351
Hoc
pol.
obtam,..f .
.)1;:
>
Wh~l1factor
common monomial factor,
•
In your owrt words:, describe-a method for'flndiag the
greatest common factor of a polynomial.
4. Explain how the word factor can be used as a noun
and a verb. Noun: Each polynomial in a product is a
Find the greatest common factor of the terms of the
polynomial by first factoring each term and then finding
the product of the common factors.
factor of the product
Verb: You can factor the greatest common
factor from each term of some polynomials.
monomial
Go to pages 392-393 to
record your assignments.
~
Developing Skills
xercises 1-16, find the greatest common
t'Iexpressions. See Examples 1 and 2.
Gz)
i.
Z2, - Z6
3;
2x2, 12x
4. 36x4, 18.il
@
6. r6s4, - rs
8. -15x6y3, 45xy3
(ii)
5
9y z4: -12y z4@
14x2,1, 7x4
'I
CD
28a4b2,
@
@
8
14a3,
of
r, t7
2.
ulv, U3V2
',.
0)
factor
_
42a2b5
10. 5y4, lOx2y2, 1
~
C[)
~
16x2y,12xy2,36x2~
2(x
+ 3), 3(x + 3)~
4(x - 5), 3x(x - 5)<r::i>
x(7x
+
5), 7x
x - 4, y(x -
+ 5<-E];>
4)<Z=i>
Exercises 17-52, factor the polynomial.
the polynomials
have no common
(Note: Some
monomial
factor.)
fl51.
Examples 3-7.
52.
1t3x+~
n!6z+3~
'. St - 16([['~-5
-
+2
-5(5x
0
iI. 24y2 - I
1'.x2+
~
{I. 25u2
..
~)
-
14«
iD
-----..3)
6 4y
2 -
18. 5y - 5 "2'--====::::"'-""
. 20. 4x - 28
~==-~:....
22. 4u + 1 '1-(u + 3
24.~
2
+
+
12~
S3 -
S ~
.
26.
8z3
28. -
~," 7s
+ 9t2
~-.~--"a--c-:-to-r~
32.9z6
+ 27z403"Z2
34. 12x2 - 5y3
~mmonfac~
form. See Example
d -5x -JQ-)
30. 36t4~
~y
2
standard
fJ 59.
+y
4
+
a negative
-
real number
and then write the polynomial
+ 3)
+1
.....-r:ft2((33tt22 + 2~\)
,.1.2x4+6~
In Exercises 53-60, factor
the polynomial
-
12x '6-x-'-~'--2)-
8.
from
factor in