7.2 factoring using the distributive property cord math mrs. spitz fall 2006
TRANSCRIPT
7.2 Factoring Using the Distributive Property
CORD MathMrs. SpitzFall 2006
Objectives:
• Use the GCF and the distributive property to factor polynomials.
• Use the information you are gaining now to get into Algebra II next year or test Math 121, so you can get into a decent college next year.
Assignment
• Pg. 263 #4-35 all
Introduction
• In chapter 6, you multiplied a polynomial by a monomial by using the distributive property. You can also reverse the process and express a polynomial in factored form by using the distributive property.
Yeah, so what does that mean?
• Multiplying Polynomials:
• Factoring polynomials:
yxy
yxyxy
xzxyzyx
baba
612
)2(3)4(3)24(3
)(
33)(3
)24(3
)2(3)4(3612
)(
)(333
xy
yxyyxy
zyxxzxy
baba
The expression 3y(4x + 2) at the right above is not considered fully factored since the polynomial 4x + 2 can be factored as 2(2x + 1). The completely factored form of 12xy and 6y would be 6y(2x + 1). Factoring a polynomial or finding the factored form of a polynomial means to find its completely factored form.
Ex. 1: Use the distributive property to factor 10y2 + 15y
• First, find the greatest common factor for 10y2 and 15y
• Then, express each term as the product of the GCF and its remaining factors.
yy
yyy
5315
5210 2
The GCF is 5y.
)32(5
)3(5)2(51510 2
yy
yyyyy
Ex. 2: Factor 21ab2 – 33a2bc
• First, find the greatest common factor for 21ab2 and 33a2bc
• Then, express each term as the product of the GCF and its remaining factors.
The GCF is 3ab.
cbaabca
bbaab
11333
73212
2
)117(3
)11(3)7(33321 22
acbab
acabbabbcaab
Ex. 3: Factor 6x3y2 + 14x2y + 2x2
• First, find the greatest common factor for 6x3y2 and 14x2y and 2x2
• Then, express each term as the product of the GCF and its remaining factors.
The GCF is 2x2.
xxx
yxxyx
yyxxxyx
22
7214
326
2
2
23
)173(2
)1(2)7(2)3(2214622
22222223
yxyx
xyxxyxxyxyx