5 . 1 polynomials 2 common factors & the gcf 24 60...
TRANSCRIPT
Polynomials 2Common Factors & the GCF
5.1
Math 10FMr. Knight
24 6012
Polynomials 2Common Factors and the GCF
If you think of a number as a product, then any numbers that you could multiply to make the product are called FACTORS.
24: 1, 2, 3, 4, 6, 8, 12, 24
30: 1, 2, 3, 5, 6, 10, 15, 30
The Greatest Common Factor (GCF) is the largest factor that iscommon to two different numbers. In this case, 6 is the biggestfactor common to both.
Try these: 16 & 24 64 & 96
5.1 date
24: 1, 2, 3, 4, 6, 8, 12, 24
30: 1, 2, 3, 5, 6, 10, 15, 30
Polynomials 2Common Factors and the GCF
The best technique for finding the GCF is to list a number's primefactors, then make a product out of the common prime factors.
This technique also works when variable factors are involved
5.1
322224 ×××=53230 ××=632 =×
yxyxyx 2223 2,4,2
yxxyxyyxxyx
yxxxyx
⋅⋅⋅=
⋅⋅⋅⋅⋅=
⋅⋅⋅⋅=
22224
22
2
22
3
GCF:
GCF: yxyxx 222 =⋅⋅⋅
The GCF will contain variablesthat have the highest degreethat can be found in EVERYoriginal product.
Assignment
Text Page 184Questions�
1-45.a odd
Polynomials 2Factoring ExpressionsWith Common Factors
5.2
Math 10FMr. Knight
146 2-x
Polynomials 2Factoring Expressions with Common Factors
Factoring an expression first involves figuring out the GCF ofeach of the expression's terms.
5.2 date
baba 223 69 −Eg. Factor:
baababbaaaba
××××=
××××××=
326339
2
23
GCF: babaa 233 =×××Once you've figured out the GCF, divide itout of each term to factor the expression.
( )233 2 −abba
Assignment
Text Page 185Questions�1 - 33 odd
Polynomials 2Multiplying a Polynomial
by a Monomial
5.3
Math 10FMr. Knight
)53(2 -- xx
Polynomials 2Multiplying a Polynomial by a Monomial
To Expand and Simplify the product of a Monomial and a Polynomial, use the Distributive Property (multiply each termoutside of the brackets times each term inside).
5.3 date
Assignment
Text Page 189Questions�1 - 47 odd
use exponent ruleswherever necessary
( )
102462108632)543(2
2
22
2
+−=
+−+−=
−−+−
xxxxxx
xxxx
watch fornegative
coefficients
collect liketerms to
finish
Polynomials 2Dividing Polynomials
by Monomials
5.4
Math 10FMr. Knight
yyyxy
3241512 2 +-
Polynomials 2Dividing Polynomials by Monomials
The Distributive Property applies to division as well as multiplication.To simplify a polynomial expression involving division, therefore, you divide EACH term in the numerator by the denominator.
5.4 date
Assignment
Text Page 190Questions�
1 - 25.c odd
yyyxy
3241512 2 +−
original expression
give eachterm in thenumerator
its owndenominator
yy
yy
yxy
324
315
312 2
+−
yy
yy
yxy
324
315
312 2
+−4 5 8
cancel whereveryou can
854 +− yx
Polynomials 2Binomial Products
5.5
Math 10FMr. Knight
( )( )1543 +- xx
Polynomials 2Binomial Products (FOIL)
To multiply two binomials, multiply EACH term in the first binomialwith EACH term in the second binomial.F - First TermsO - Outside TermsI - Inside TermsL - Last Terms
5.5 date
Assignment
Text Page 194Questions�1 - 57 odd
( )( )1543 +− xx
15x2
-4
3x
-20x
FO
IL
41715420315
2
2
−−
−−+
xxxxx
The inside andoutside productswill be like terms.
Collect themto finish off.
Polynomials 2Factoring Trinomials
5.6
Math 10FMr. Knight
16102 +- xx
Polynomials 2Factoring Trinomials
To factor a trinomial, think back to how it was built...(the product oftwo binomials/FOIL). We took a binomial, found the first, outside,inside, and last products, and collected like terms.Now we have to work in reverse and ask ourselves...
5.6 date
16102 +− xx
( )± ( )± what two FIRST TERMSwould multiply to give me x2?
what two LAST TERMSwould multiply to 16AND add -10?
X X
( )± ( )±
( )( )X X- 2 - 8
( )( )
16101628
82
2
2
+−
+−−
−−
xxxxx
xxcheck using FOIL...
Polynomials 2Factoring Trinomials
Sometimes you have to factor out a GCF first...
5.6
Assignment
Text Page 197Questions�3-45 odd
( )35227042
2
2
−−
−−
xxxx
GCF
what two numbers willmultiply to -35 and add to -2?
( )( )572 +− xx